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

Percentage Accurate: 98.3% → 100.0%

Time: 3.9s

Alternatives: 8

Speedup: 1.3×

• 20.0% 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: 98.3% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma((y + z), x, -z);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative 98.8%

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

   2. sub-neg 98.8%

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

   3. metadata-eval 98.8%

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

   4. distribute-rgt-in 98.8%

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

   5. neg-mul-1 98.8%

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

   6. associate-+l+ 98.8%

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

   7. distribute-lft-in 100.0%

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

   8. *-commutative 100.0%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-99}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+20} \lor \neg \left(x \leq 2.2 \cdot 10^{+87}\right) \land x \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+190)
   (* z x)
   (if (<= x -2.2e+128)
     (* y x)
     (if (<= x -5.4e+57)
       (* z x)
       (if (<= x -5.7e-14)
         (* y x)
         (if (<= x 8e-99)
           (- z)
           (if (or (<= x 1.25e+20) (and (not (<= x 2.2e+87)) (<= x 4.8e+141)))
             (* y x)
             (* z x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+190) {
		tmp = z * x;
	} else if (x <= -2.2e+128) {
		tmp = y * x;
	} else if (x <= -5.4e+57) {
		tmp = z * x;
	} else if (x <= -5.7e-14) {
		tmp = y * x;
	} else if (x <= 8e-99) {
		tmp = -z;
	} else if ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141))) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	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 <= (-7.5d+190)) then
        tmp = z * x
    else if (x <= (-2.2d+128)) then
        tmp = y * x
    else if (x <= (-5.4d+57)) then
        tmp = z * x
    else if (x <= (-5.7d-14)) then
        tmp = y * x
    else if (x <= 8d-99) then
        tmp = -z
    else if ((x <= 1.25d+20) .or. (.not. (x <= 2.2d+87)) .and. (x <= 4.8d+141)) then
        tmp = y * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+190) {
		tmp = z * x;
	} else if (x <= -2.2e+128) {
		tmp = y * x;
	} else if (x <= -5.4e+57) {
		tmp = z * x;
	} else if (x <= -5.7e-14) {
		tmp = y * x;
	} else if (x <= 8e-99) {
		tmp = -z;
	} else if ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141))) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+190:
		tmp = z * x
	elif x <= -2.2e+128:
		tmp = y * x
	elif x <= -5.4e+57:
		tmp = z * x
	elif x <= -5.7e-14:
		tmp = y * x
	elif x <= 8e-99:
		tmp = -z
	elif (x <= 1.25e+20) or (not (x <= 2.2e+87) and (x <= 4.8e+141)):
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+190)
		tmp = Float64(z * x);
	elseif (x <= -2.2e+128)
		tmp = Float64(y * x);
	elseif (x <= -5.4e+57)
		tmp = Float64(z * x);
	elseif (x <= -5.7e-14)
		tmp = Float64(y * x);
	elseif (x <= 8e-99)
		tmp = Float64(-z);
	elseif ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141)))
		tmp = Float64(y * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+190)
		tmp = z * x;
	elseif (x <= -2.2e+128)
		tmp = y * x;
	elseif (x <= -5.4e+57)
		tmp = z * x;
	elseif (x <= -5.7e-14)
		tmp = y * x;
	elseif (x <= 8e-99)
		tmp = -z;
	elseif ((x <= 1.25e+20) || (~((x <= 2.2e+87)) && (x <= 4.8e+141)))
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+190], N[(z * x), $MachinePrecision], If[LessEqual[x, -2.2e+128], N[(y * x), $MachinePrecision], If[LessEqual[x, -5.4e+57], N[(z * x), $MachinePrecision], If[LessEqual[x, -5.7e-14], N[(y * x), $MachinePrecision], If[LessEqual[x, 8e-99], (-z), If[Or[LessEqual[x, 1.25e+20], And[N[Not[LessEqual[x, 2.2e+87]], $MachinePrecision], LessEqual[x, 4.8e+141]]], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4999999999999994e190 or -2.20000000000000017e128 < x < -5.3999999999999997e57 or 1.25e20 < x < 2.2000000000000001e87 or 4.79999999999999995e141 < x

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.3%

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

   if -7.4999999999999994e190 < x < -2.20000000000000017e128 or -5.3999999999999997e57 < x < -5.69999999999999969e-14 or 8.0000000000000002e-99 < x < 1.25e20 or 2.2000000000000001e87 < x < 4.79999999999999995e141

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.1%

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

   if -5.69999999999999969e-14 < x < 8.0000000000000002e-99

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.4%

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

      1. neg-mul-1 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-14}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-99}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+20} \lor \neg \left(x \leq 2.2 \cdot 10^{+87}\right) \land x \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-14) (not (<= x 8e-99))) (* (+ y z) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-14) || !(x <= 8e-99)) {
		tmp = (y + z) * x;
	} 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 <= (-6d-14)) .or. (.not. (x <= 8d-99))) then
        tmp = (y + z) * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-14) || !(x <= 8e-99)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-14) or not (x <= 8e-99):
		tmp = (y + z) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-14) || !(x <= 8e-99))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e-14) || ~((x <= 8e-99)))
		tmp = (y + z) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-14], N[Not[LessEqual[x, 8e-99]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999997e-14 or 8.0000000000000002e-99 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

   4. Simplified 95.2%

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

   if -5.9999999999999997e-14 < x < 8.0000000000000002e-99

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.4%

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

      1. neg-mul-1 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-14} \lor \neg \left(x \leq 3.4 \cdot 10^{-91}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e-14) (not (<= x 3.4e-91))) (* (+ y z) x) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-14) || !(x <= 3.4e-91)) {
		tmp = (y + z) * x;
	} 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 <= (-3.3d-14)) .or. (.not. (x <= 3.4d-91))) then
        tmp = (y + z) * x
    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 <= -3.3e-14) || !(x <= 3.4e-91)) {
		tmp = (y + z) * x;
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e-14) or not (x <= 3.4e-91):
		tmp = (y + z) * x
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e-14) || !(x <= 3.4e-91))
		tmp = Float64(Float64(y + z) * x);
	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 <= -3.3e-14) || ~((x <= 3.4e-91)))
		tmp = (y + z) * x;
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e-14], N[Not[LessEqual[x, 3.4e-91]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999998e-14 or 3.40000000000000027e-91 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

   4. Simplified 95.2%

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

   if -3.2999999999999998e-14 < x < 3.40000000000000027e-91

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-14} \lor \neg \left(x \leq 3.4 \cdot 10^{-91}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-14} \lor \neg \left(x \leq 1.25 \cdot 10^{-96}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e-14) (not (<= x 1.25e-96))) (* (+ y z) x) (- (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-14) || !(x <= 1.25e-96)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * 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 <= (-1.55d-14)) .or. (.not. (x <= 1.25d-96))) then
        tmp = (y + z) * x
    else
        tmp = (z * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-14) || !(x <= 1.25e-96)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e-14) or not (x <= 1.25e-96):
		tmp = (y + z) * x
	else:
		tmp = (z * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e-14) || !(x <= 1.25e-96))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(Float64(z * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55e-14) || ~((x <= 1.25e-96)))
		tmp = (y + z) * x;
	else
		tmp = (z * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e-14], N[Not[LessEqual[x, 1.25e-96]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-14 or 1.24999999999999999e-96 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

   4. Simplified 95.2%

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

   if -1.55000000000000002e-14 < x < 1.24999999999999999e-96

   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. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 78.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-14} \lor \neg \left(x \leq 1.25 \cdot 10^{-96}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \]

Alternative 6: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{-90}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-14) (not (<= x 4e-90))) (* y x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-14) || !(x <= 4e-90)) {
		tmp = y * x;
	} 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-14)) .or. (.not. (x <= 4d-90))) then
        tmp = y * x
    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-14) || !(x <= 4e-90)) {
		tmp = y * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-14) or not (x <= 4e-90):
		tmp = y * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-14) || !(x <= 4e-90))
		tmp = Float64(y * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e-14) || ~((x <= 4e-90)))
		tmp = y * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-14], N[Not[LessEqual[x, 4e-90]], $MachinePrecision]], N[(y * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e-14 or 3.99999999999999998e-90 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 51.7%

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

   if -4.8e-14 < x < 3.99999999999999998e-90

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.4%

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

      1. neg-mul-1 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{-90}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. *-commutative 98.8%

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

   2. distribute-rgt-out-- 98.8%

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

   3. cancel-sign-sub-inv 98.8%

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

   4. metadata-eval 98.8%

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

   5. neg-mul-1 98.8%

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

   6. associate-+r+ 98.8%

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

   7. unsub-neg 98.8%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 8: 36.9% 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 98.8%

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

2. Taylor expanded in x around 0 39.7%

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

   1. neg-mul-1 39.7%

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

4. Simplified 39.7%

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

5. Final simplification 39.7%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))