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

Percentage Accurate: 97.7% → 100.0%

Time: 7.9s

Alternatives: 7

Speedup: 1.3×

• 21.3% 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: 97.7% 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 97.3%

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

   1. *-commutative 97.3%

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

   2. sub-neg 97.3%

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

   3. distribute-rgt-in 97.3%

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

   4. metadata-eval 97.3%

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

   5. neg-mul-1 97.3%

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

   6. associate-+r+ 97.3%

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

   7. unsub-neg 97.3%

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

   8. +-commutative 97.3%

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

   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. Add Preprocessing

Alternative 2: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5200:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e+100)
   (* x z)
   (if (<= x -6.8e-13) (* x y) (if (<= x 5200.0) (- z) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+100) {
		tmp = x * z;
	} else if (x <= -6.8e-13) {
		tmp = x * y;
	} else if (x <= 5200.0) {
		tmp = -z;
	} 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 <= (-1.6d+100)) then
        tmp = x * z
    else if (x <= (-6.8d-13)) then
        tmp = x * y
    else if (x <= 5200.0d0) then
        tmp = -z
    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 <= -1.6e+100) {
		tmp = x * z;
	} else if (x <= -6.8e-13) {
		tmp = x * y;
	} else if (x <= 5200.0) {
		tmp = -z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+100:
		tmp = x * z
	elif x <= -6.8e-13:
		tmp = x * y
	elif x <= 5200.0:
		tmp = -z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+100)
		tmp = Float64(x * z);
	elseif (x <= -6.8e-13)
		tmp = Float64(x * y);
	elseif (x <= 5200.0)
		tmp = Float64(-z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+100)
		tmp = x * z;
	elseif (x <= -6.8e-13)
		tmp = x * y;
	elseif (x <= 5200.0)
		tmp = -z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+100], N[(x * z), $MachinePrecision], If[LessEqual[x, -6.8e-13], N[(x * y), $MachinePrecision], If[LessEqual[x, 5200.0], (-z), N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5999999999999999e100 or 5200 < x

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. sub-neg 92.8%

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

      3. distribute-rgt-in 92.8%

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

      4. metadata-eval 92.8%

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

      5. neg-mul-1 92.8%

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

      6. associate-+r+ 92.8%

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

      7. unsub-neg 92.8%

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

      8. +-commutative 92.8%

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

      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 z around inf 59.2%

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

   6. Taylor expanded in x around inf 58.2%

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

      1. *-commutative 58.2%

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

   8. Simplified 58.2%

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

   if -1.5999999999999999e100 < x < -6.80000000000000031e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 71.4%

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

   if -6.80000000000000031e-13 < x < 5200

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.3%

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

   6. Taylor expanded in x around 0 72.3%

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

      1. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5200:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \lor \neg \left(x \leq 1.35 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.6) (not (<= x 1.35e-14))) (* x (+ z y)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6) || !(x <= 1.35e-14)) {
		tmp = x * (z + y);
	} 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 <= (-8.6d0)) .or. (.not. (x <= 1.35d-14))) then
        tmp = x * (z + y)
    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 <= -8.6) || !(x <= 1.35e-14)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.6) or not (x <= 1.35e-14):
		tmp = x * (z + y)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.6) || !(x <= 1.35e-14))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.6) || ~((x <= 1.35e-14)))
		tmp = x * (z + y);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.6], N[Not[LessEqual[x, 1.35e-14]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.59999999999999964 or 1.3499999999999999e-14 < x

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   if -8.59999999999999964 < x < 1.3499999999999999e-14

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \lor \neg \left(x \leq 1.35 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-13} \lor \neg \left(x \leq 7.4 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-13) (not (<= x 7.4e-15))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-13) || !(x <= 7.4e-15)) {
		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 <= (-5.8d-13)) .or. (.not. (x <= 7.4d-15))) 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 <= -5.8e-13) || !(x <= 7.4e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-13) or not (x <= 7.4e-15):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-13) || !(x <= 7.4e-15))
		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 <= -5.8e-13) || ~((x <= 7.4e-15)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-13], N[Not[LessEqual[x, 7.4e-15]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999995e-13 or 7.40000000000000034e-15 < x

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   if -5.7999999999999995e-13 < x < 7.40000000000000034e-15

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. neg-mul-1 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-13} \lor \neg \left(x \leq 7.4 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-13} \lor \neg \left(x \leq 8.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e-13) (not (<= x 8.2e-15))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-13) || !(x <= 8.2e-15)) {
		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-13)) .or. (.not. (x <= 8.2d-15))) 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-13) || !(x <= 8.2e-15)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e-13) or not (x <= 8.2e-15):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e-13) || !(x <= 8.2e-15))
		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-13) || ~((x <= 8.2e-15)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e-13], N[Not[LessEqual[x, 8.2e-15]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000002e-13 or 8.20000000000000072e-15 < x

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 49.4%

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

   if -8.0000000000000002e-13 < x < 8.20000000000000072e-15

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. neg-mul-1 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-13} \lor \neg \left(x \leq 8.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.3% 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 97.3%

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

   1. *-commutative 97.3%

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

   2. sub-neg 97.3%

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

   3. distribute-rgt-in 97.3%

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

   4. metadata-eval 97.3%

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

   5. neg-mul-1 97.3%

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

   6. associate-+r+ 97.3%

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

   7. unsub-neg 97.3%

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

   8. +-commutative 97.3%

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

   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 z around 0 76.7%

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

6. Taylor expanded in x around 0 41.3%

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

   1. neg-mul-1 41.3%

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

8. Simplified 41.3%

   \[\leadsto \color{blue}{-z} \]
9. Add Preprocessing

Alternative 7: 2.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 97.3%

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

   1. *-commutative 97.3%

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

   2. sub-neg 97.3%

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

   3. distribute-rgt-in 97.3%

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

   4. metadata-eval 97.3%

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

   5. neg-mul-1 97.3%

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

   6. associate-+r+ 97.3%

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

   7. unsub-neg 97.3%

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

   8. +-commutative 97.3%

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

   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 z around 0 76.7%

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

6. Taylor expanded in x around 0 41.3%

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

   1. neg-mul-1 41.3%

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

8. Simplified 41.3%

   \[\leadsto \color{blue}{-z} \]
9. Step-by-step derivation

   1. add-sqr-sqrt 25.2%

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

   2. sqrt-unprod 17.9%

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

   3. sqr-neg 17.9%

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

   4. sqrt-unprod 1.2%

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

   5. add-log-exp 4.0%

      \[\leadsto \color{blue}{\log \left(e^{\sqrt{z} \cdot \sqrt{z}}\right)} \]

   6. add-sqr-sqrt 8.8%

      \[\leadsto \log \left(e^{\color{blue}{z}}\right) \]

   7. add-sqr-sqrt 8.8%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{z}} \cdot \sqrt{e^{z}}\right)} \]

   8. sqrt-unprod 8.8%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{z} \cdot e^{z}}\right)} \]

   9. *-un-lft-identity 8.8%

      \[\leadsto \log \left(\sqrt{e^{z} \cdot e^{\color{blue}{1 \cdot z}}}\right) \]

   10. exp-prod 8.8%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot \color{blue}{{\left(e^{1}\right)}^{z}}}\right) \]

   11. add-sqr-sqrt 4.0%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}}}\right) \]

   12. sqrt-unprod 5.0%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{z \cdot z}\right)}}}\right) \]

   13. sqr-neg 5.0%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot {\left(e^{1}\right)}^{\left(\sqrt{\color{blue}{\left(-z\right) \cdot \left(-z\right)}}\right)}}\right) \]

   14. sqrt-unprod 1.0%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}}}\right) \]

   15. add-sqr-sqrt 1.6%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(-z\right)}}}\right) \]

   16. exp-prod 1.6%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot \color{blue}{e^{1 \cdot \left(-z\right)}}}\right) \]

   17. *-un-lft-identity 1.6%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot e^{\color{blue}{-z}}}\right) \]

   18. exp-neg 1.6%

       \[\leadsto \log \left(\sqrt{e^{z} \cdot \color{blue}{\frac{1}{e^{z}}}}\right) \]

   19. rgt-mult-inverse 2.7%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

   20. metadata-eval 2.7%

       \[\leadsto \log \color{blue}{1} \]

   21. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \]

10. Applied egg-rr 2.7%

    \[\leadsto \color{blue}{0} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024147 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))