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

Percentage Accurate: 98.1% → 100.0%

Time: 4.1s

Alternatives: 7

Speedup: 1.4×

• 20.4% 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: 98.1% 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, 1.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1 \cdot z + x \cdot \left(y + z\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 0.00096:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -32000000000.0)
   (* z x)
   (if (<= x -8.8e-104) (* y x) (if (<= x 0.00096) (- z) (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -32000000000.0) {
		tmp = z * x;
	} else if (x <= -8.8e-104) {
		tmp = y * x;
	} else if (x <= 0.00096) {
		tmp = -z;
	} else {
		tmp = y * 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 <= (-32000000000.0d0)) then
        tmp = z * x
    else if (x <= (-8.8d-104)) then
        tmp = y * x
    else if (x <= 0.00096d0) then
        tmp = -z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -32000000000.0) {
		tmp = z * x;
	} else if (x <= -8.8e-104) {
		tmp = y * x;
	} else if (x <= 0.00096) {
		tmp = -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -32000000000.0:
		tmp = z * x
	elif x <= -8.8e-104:
		tmp = y * x
	elif x <= 0.00096:
		tmp = -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -32000000000.0)
		tmp = Float64(z * x);
	elseif (x <= -8.8e-104)
		tmp = Float64(y * x);
	elseif (x <= 0.00096)
		tmp = Float64(-z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -32000000000.0)
		tmp = z * x;
	elseif (x <= -8.8e-104)
		tmp = y * x;
	elseif (x <= 0.00096)
		tmp = -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -32000000000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, -8.8e-104], N[(y * x), $MachinePrecision], If[LessEqual[x, 0.00096], (-z), N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e10

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z \cdot \left(x - 1\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 57.9

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

   5. Applied rewrites 57.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 57.4%

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

   if -3.2e10 < x < -8.80000000000000047e-104 or 9.60000000000000024e-4 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 4.5

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

   5. Applied rewrites 4.5%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.3

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

   8. Applied rewrites 62.3%

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

   if -8.80000000000000047e-104 < x < 9.60000000000000024e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 78.1

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

   5. Applied rewrites 78.1%

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

Alternative 3: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-145}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00125:\\ \;\;\;\;\left(x - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -1.5e-145) t_0 (if (<= x 0.00125) (* (- x 1.0) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.5e-145) {
		tmp = t_0;
	} else if (x <= 0.00125) {
		tmp = (x - 1.0) * z;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (z + y) * x
    if (x <= (-1.5d-145)) then
        tmp = t_0
    else if (x <= 0.00125d0) then
        tmp = (x - 1.0d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.5e-145) {
		tmp = t_0;
	} else if (x <= 0.00125) {
		tmp = (x - 1.0) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + y) * x
	tmp = 0
	if x <= -1.5e-145:
		tmp = t_0
	elif x <= 0.00125:
		tmp = (x - 1.0) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z + y) * x)
	tmp = 0.0
	if (x <= -1.5e-145)
		tmp = t_0;
	elseif (x <= 0.00125)
		tmp = Float64(Float64(x - 1.0) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z + y) * x;
	tmp = 0.0;
	if (x <= -1.5e-145)
		tmp = t_0;
	elseif (x <= 0.00125)
		tmp = (x - 1.0) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.5e-145], t$95$0, If[LessEqual[x, 0.00125], N[(N[(x - 1.0), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999996e-145 or 0.00125000000000000003 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 96.5

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

   5. Applied rewrites 96.5%

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

   if -1.49999999999999996e-145 < x < 0.00125000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z \cdot \left(x - 1\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.6

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

   5. Applied rewrites 79.6%

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

Alternative 4: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-145}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00096:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -1.5e-145) t_0 (if (<= x 0.00096) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.5e-145) {
		tmp = t_0;
	} else if (x <= 0.00096) {
		tmp = -z;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (z + y) * x
    if (x <= (-1.5d-145)) then
        tmp = t_0
    else if (x <= 0.00096d0) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.5e-145) {
		tmp = t_0;
	} else if (x <= 0.00096) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + y) * x
	tmp = 0
	if x <= -1.5e-145:
		tmp = t_0
	elif x <= 0.00096:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z + y) * x)
	tmp = 0.0
	if (x <= -1.5e-145)
		tmp = t_0;
	elseif (x <= 0.00096)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z + y) * x;
	tmp = 0.0;
	if (x <= -1.5e-145)
		tmp = t_0;
	elseif (x <= 0.00096)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.5e-145], t$95$0, If[LessEqual[x, 0.00096], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999996e-145 or 9.60000000000000024e-4 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 96.5

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

   5. Applied rewrites 96.5%

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

   if -1.49999999999999996e-145 < x < 9.60000000000000024e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 79.0

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

   5. Applied rewrites 79.0%

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

Alternative 5: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 0.031:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -14.0) (* z x) (if (<= x 0.031) (- z) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -14.0) {
		tmp = z * x;
	} else if (x <= 0.031) {
		tmp = -z;
	} 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 <= (-14.0d0)) then
        tmp = z * x
    else if (x <= 0.031d0) then
        tmp = -z
    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 <= -14.0) {
		tmp = z * x;
	} else if (x <= 0.031) {
		tmp = -z;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -14.0:
		tmp = z * x
	elif x <= 0.031:
		tmp = -z
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -14.0)
		tmp = Float64(z * x);
	elseif (x <= 0.031)
		tmp = Float64(-z);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -14.0)
		tmp = z * x;
	elseif (x <= 0.031)
		tmp = -z;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -14.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 0.031], (-z), N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -14 or 0.031 < x

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z \cdot \left(x - 1\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.1

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.4%

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

   if -14 < x < 0.031

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 70.3

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

   5. Applied rewrites 70.3%

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

Alternative 6: 36.5% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 39.1

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

5. Applied rewrites 39.1%

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

Alternative 7: 2.6% accurate, 17.0× 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 z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 39.1

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

5. Applied rewrites 39.1%

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

7. Applied rewrites 2.6%

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

Reproduce

herbie shell --seed 2024294 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))