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

Percentage Accurate: 97.6% → 100.0%

Time: 5.6s

Alternatives: 7

Speedup: 1.4×

• 20.1% 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: 97.6% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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. accelerator-lowering-fma.f64 N/A

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

   3. +-commutative N/A

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

   4. +-lowering-+.f64 N/A

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

   5. mul-1-neg N/A

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

   6. neg-lowering-neg.f64 100.0

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

5. Simplified 100.0%

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

Alternative 2: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+175}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-71}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+175)
   (* x y)
   (if (<= x -1.26e+62)
     (* x z)
     (if (<= x -9.5e-37) (* x y) (if (<= x 1e-71) (- z) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+175) {
		tmp = x * y;
	} else if (x <= -1.26e+62) {
		tmp = x * z;
	} else if (x <= -9.5e-37) {
		tmp = x * y;
	} else if (x <= 1e-71) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.5d+175)) then
        tmp = x * y
    else if (x <= (-1.26d+62)) then
        tmp = x * z
    else if (x <= (-9.5d-37)) then
        tmp = x * y
    else if (x <= 1d-71) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+175) {
		tmp = x * y;
	} else if (x <= -1.26e+62) {
		tmp = x * z;
	} else if (x <= -9.5e-37) {
		tmp = x * y;
	} else if (x <= 1e-71) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+175:
		tmp = x * y
	elif x <= -1.26e+62:
		tmp = x * z
	elif x <= -9.5e-37:
		tmp = x * y
	elif x <= 1e-71:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+175)
		tmp = Float64(x * y);
	elseif (x <= -1.26e+62)
		tmp = Float64(x * z);
	elseif (x <= -9.5e-37)
		tmp = Float64(x * y);
	elseif (x <= 1e-71)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+175)
		tmp = x * y;
	elseif (x <= -1.26e+62)
		tmp = x * z;
	elseif (x <= -9.5e-37)
		tmp = x * y;
	elseif (x <= 1e-71)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+175], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.26e+62], N[(x * z), $MachinePrecision], If[LessEqual[x, -9.5e-37], N[(x * y), $MachinePrecision], If[LessEqual[x, 1e-71], (-z), N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000001e175 or -1.25999999999999995e62 < x < -9.49999999999999927e-37 or 9.9999999999999992e-72 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 57.1

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

   5. Simplified 57.1%

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

   if -7.5000000000000001e175 < x < -1.25999999999999995e62

   1. Initial program 96.7%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 65.6

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

   8. Simplified 65.6%

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

   if -9.49999999999999927e-37 < x < 9.9999999999999992e-72

   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. neg-lowering-neg.f64 77.4

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

   5. Simplified 77.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+175}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-71}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -150:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x, y, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -150.0) t_0 (if (<= x 1.0) (fma x y (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -150.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = fma(x, y, -z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -150.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = fma(x, y, Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -150.0], t$95$0, If[LessEqual[x, 1.0], N[(x * y + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -150 or 1 < x

   1. Initial program 93.3%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.9

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

   5. Simplified 98.9%

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

   if -150 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{y}, \mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 97.8%

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

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-46}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -6.6e-33) t_0 (if (<= x 1.05e-46) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -6.6e-33) {
		tmp = t_0;
	} else if (x <= 1.05e-46) {
		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 = x * (z + y)
    if (x <= (-6.6d-33)) then
        tmp = t_0
    else if (x <= 1.05d-46) 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 = x * (z + y);
	double tmp;
	if (x <= -6.6e-33) {
		tmp = t_0;
	} else if (x <= 1.05e-46) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -6.6e-33:
		tmp = t_0
	elif x <= 1.05e-46:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -6.6e-33)
		tmp = t_0;
	elseif (x <= 1.05e-46)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -6.6e-33)
		tmp = t_0;
	elseif (x <= 1.05e-46)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e-33], t$95$0, If[LessEqual[x, 1.05e-46], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6000000000000005e-33 or 1.04999999999999994e-46 < 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

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 94.7

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

   5. Simplified 94.7%

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

   if -6.6000000000000005e-33 < x < 1.04999999999999994e-46

   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. neg-lowering-neg.f64 76.4

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

   5. Simplified 76.4%

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

Alternative 5: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-72}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e-32) (* x y) (if (<= x 9.6e-72) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-32) {
		tmp = x * y;
	} else if (x <= 9.6e-72) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.2d-32)) then
        tmp = x * y
    else if (x <= 9.6d-72) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-32) {
		tmp = x * y;
	} else if (x <= 9.6e-72) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e-32:
		tmp = x * y
	elif x <= 9.6e-72:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e-32)
		tmp = Float64(x * y);
	elseif (x <= 9.6e-72)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.2e-32)
		tmp = x * y;
	elseif (x <= 9.6e-72)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e-32], N[(x * y), $MachinePrecision], If[LessEqual[x, 9.6e-72], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2000000000000001e-32 or 9.6e-72 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 53.5

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

   5. Simplified 53.5%

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

   if -1.2000000000000001e-32 < x < 9.6e-72

   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. neg-lowering-neg.f64 77.4

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

   5. Simplified 77.4%

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

Alternative 6: 36.8% 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 96.5%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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. neg-lowering-neg.f64 34.6

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

5. Simplified 34.6%

   \[\leadsto \color{blue}{-z} \]
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 96.5%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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. neg-lowering-neg.f64 34.6

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

5. Simplified 34.6%

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

   1. neg-sub0 N/A

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

   2. flip-- N/A

      \[\leadsto \color{blue}{\frac{0 \cdot 0 - z \cdot z}{0 + z}} \]

7. Applied egg-rr 2.6%

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

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))