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

Percentage Accurate: 98.0% → 100.0%

Time: 4.9s

Alternatives: 8

Speedup: 1.3×

• 20.5% 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, 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 98.0%

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

   1. *-commutative 98.0%

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

   2. sub-neg 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. metadata-eval 98.0%

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

   5. neg-mul-1 98.0%

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

   6. associate-+r+ 98.0%

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

   7. unsub-neg 98.0%

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

   8. +-commutative 98.0%

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

   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. Final simplification 100.0%

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

Alternative 2: 61.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+285}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-39} \lor \neg \left(x \leq 5.4 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+285)
   (* x z)
   (if (or (<= x -3e-39) (not (<= x 5.4e-66))) (* x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+285) {
		tmp = x * z;
	} else if ((x <= -3e-39) || !(x <= 5.4e-66)) {
		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 <= (-4.2d+285)) then
        tmp = x * z
    else if ((x <= (-3d-39)) .or. (.not. (x <= 5.4d-66))) 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 <= -4.2e+285) {
		tmp = x * z;
	} else if ((x <= -3e-39) || !(x <= 5.4e-66)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e+285:
		tmp = x * z
	elif (x <= -3e-39) or not (x <= 5.4e-66):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+285)
		tmp = Float64(x * z);
	elseif ((x <= -3e-39) || !(x <= 5.4e-66))
		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 <= -4.2e+285)
		tmp = x * z;
	elseif ((x <= -3e-39) || ~((x <= 5.4e-66)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+285], N[(x * z), $MachinePrecision], If[Or[LessEqual[x, -3e-39], N[Not[LessEqual[x, 5.4e-66]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e285

   1. Initial program 71.2%

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

      1. *-commutative 71.2%

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

      2. sub-neg 71.2%

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

      3. distribute-rgt-in 71.2%

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

      4. metadata-eval 71.2%

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

      5. neg-mul-1 71.2%

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

      6. associate-+r+ 71.2%

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

      7. unsub-neg 71.2%

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

      8. +-commutative 71.2%

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

      9. distribute-lft-out 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 80.4%

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

   6. Taylor expanded in x around inf 80.4%

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

      1. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   if -4.2e285 < x < -3.00000000000000028e-39 or 5.39999999999999992e-66 < x

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 63.6%

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

   if -3.00000000000000028e-39 < x < 5.39999999999999992e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+285}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-39} \lor \neg \left(x \leq 5.4 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-53} \lor \neg \left(x \leq 5.3 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e-53) (not (<= x 5.3e-23))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e-53) || !(x <= 5.3e-23)) {
		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 <= (-6.8d-53)) .or. (.not. (x <= 5.3d-23))) 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 <= -6.8e-53) || !(x <= 5.3e-23)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e-53) or not (x <= 5.3e-23):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e-53) || !(x <= 5.3e-23))
		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 <= -6.8e-53) || ~((x <= 5.3e-23)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e-53], N[Not[LessEqual[x, 5.3e-23]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e-53 or 5.30000000000000042e-23 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 93.5%

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

      1. +-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -6.8e-53 < x < 5.30000000000000042e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-53} \lor \neg \left(x \leq 5.3 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.1 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-5) (not (<= x 1.1e-12))) (* x (+ z y)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-5) || !(x <= 1.1e-12)) {
		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 <= (-1.5d-5)) .or. (.not. (x <= 1.1d-12))) 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 <= -1.5e-5) || !(x <= 1.1e-12)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-5) or not (x <= 1.1e-12):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-5) || !(x <= 1.1e-12))
		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 <= -1.5e-5) || ~((x <= 1.1e-12)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-5], N[Not[LessEqual[x, 1.1e-12]], $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 < -1.50000000000000004e-5 or 1.09999999999999996e-12 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if -1.50000000000000004e-5 < x < 1.09999999999999996e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.1 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0036 \lor \neg \left(x \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0036) (not (<= x 2.8e-9))) (* x (+ z y)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0036) || !(x <= 2.8e-9)) {
		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 <= (-0.0036d0)) .or. (.not. (x <= 2.8d-9))) 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 <= -0.0036) || !(x <= 2.8e-9)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0036) or not (x <= 2.8e-9):
		tmp = x * (z + y)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0036) || !(x <= 2.8e-9))
		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 <= -0.0036) || ~((x <= 2.8e-9)))
		tmp = x * (z + y);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0036], N[Not[LessEqual[x, 2.8e-9]], $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 < -0.0035999999999999999 or 2.79999999999999984e-9 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if -0.0035999999999999999 < x < 2.79999999999999984e-9

   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 y around 0 72.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0036 \lor \neg \left(x \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -26000 \lor \neg \left(x \leq 0.00046\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -26000.0) (not (<= x 0.00046))) (* x (+ z y)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -26000.0) || !(x <= 0.00046)) {
		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 <= (-26000.0d0)) .or. (.not. (x <= 0.00046d0))) 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 <= -26000.0) || !(x <= 0.00046)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -26000.0) or not (x <= 0.00046):
		tmp = x * (z + y)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -26000.0) || !(x <= 0.00046))
		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 <= -26000.0) || ~((x <= 0.00046)))
		tmp = x * (z + y);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -26000.0], N[Not[LessEqual[x, 0.00046]], $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 < -26000 or 4.6000000000000001e-4 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if -26000 < x < 4.6000000000000001e-4

   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 y around inf 94.8%

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

      1. associate-/l* 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in z around 0 98.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -26000 \lor \neg \left(x \leq 0.00046\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-39} \lor \neg \left(x \leq 2.3 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-39) (not (<= x 2.3e-63))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-39) || !(x <= 2.3e-63)) {
		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 <= (-4.8d-39)) .or. (.not. (x <= 2.3d-63))) 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 <= -4.8e-39) || !(x <= 2.3e-63)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-39) or not (x <= 2.3e-63):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-39) || !(x <= 2.3e-63))
		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 <= -4.8e-39) || ~((x <= 2.3e-63)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-39], N[Not[LessEqual[x, 2.3e-63]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.80000000000000031e-39 or 2.3e-63 < x

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 61.4%

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

   if -4.80000000000000031e-39 < x < 2.3e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-39} \lor \neg \left(x \leq 2.3 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.7% 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 98.0%

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

3. Taylor expanded in x around 0 37.4%

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

   1. neg-mul-1 37.4%

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

5. Simplified 37.4%

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

6. Final simplification 37.4%

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

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))