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

Percentage Accurate: 97.8% → 100.0%

Time: 8.8s

Alternatives: 8

Speedup: 1.4×

• 21.1% 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: 97.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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. distribute-lft-in N/A

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

   3. associate-+l+ N/A

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

   4. *-rgt-identity N/A

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

   5. *-inverses N/A

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

   6. associate-/l* N/A

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

   7. associate-*l/ N/A

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

   8. remove-double-neg N/A

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

   9. mul-1-neg N/A

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

   10. distribute-lft-neg-in N/A

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

   11. *-commutative N/A

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

   12. mul-1-neg N/A

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

   13. unsub-neg N/A

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

   14. associate-+r- N/A

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

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + y, 0\right) - z} \]
6. Step-by-step derivation

   1. +-rgt-identity N/A

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

   2. *-commutative N/A

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

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

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

   4. +-lowering-+.f64 100.0

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

7. Applied egg-rr 100.0%

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

Alternative 2: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-20)
   (* y x)
   (if (<= y -5e-83) (- 0.0 z) (if (<= y 7.5e-55) (* z x) (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-20) {
		tmp = y * x;
	} else if (y <= -5e-83) {
		tmp = 0.0 - z;
	} else if (y <= 7.5e-55) {
		tmp = z * x;
	} 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 (y <= (-4.8d-20)) then
        tmp = y * x
    else if (y <= (-5d-83)) then
        tmp = 0.0d0 - z
    else if (y <= 7.5d-55) then
        tmp = z * x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-20) {
		tmp = y * x;
	} else if (y <= -5e-83) {
		tmp = 0.0 - z;
	} else if (y <= 7.5e-55) {
		tmp = z * x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-20:
		tmp = y * x
	elif y <= -5e-83:
		tmp = 0.0 - z
	elif y <= 7.5e-55:
		tmp = z * x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-20)
		tmp = Float64(y * x);
	elseif (y <= -5e-83)
		tmp = Float64(0.0 - z);
	elseif (y <= 7.5e-55)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.8e-20)
		tmp = y * x;
	elseif (y <= -5e-83)
		tmp = 0.0 - z;
	elseif (y <= 7.5e-55)
		tmp = z * x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-20], N[(y * x), $MachinePrecision], If[LessEqual[y, -5e-83], N[(0.0 - z), $MachinePrecision], If[LessEqual[y, 7.5e-55], N[(z * x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999986e-20 or 7.50000000000000023e-55 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot y + 0} \]

      2. accelerator-lowering-fma.f64 71.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]

   5. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 71.1

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

   7. Applied egg-rr 71.1%

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

   if -4.79999999999999986e-20 < y < -5e-83

   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-sub0 N/A

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

      3. --lowering--.f64 74.7

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

   5. Simplified 74.7%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 74.7

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

   7. Applied egg-rr 74.7%

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

   if -5e-83 < y < 7.50000000000000023e-55

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + z, 0\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

      4. +-lowering-+.f64 69.5

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + y, 0\right)} \]

   6. Taylor expanded in z around inf

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

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 55.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x, 0\right)} \]

   8. Simplified 55.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x, 0\right)} \]
   9. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. remove-double-neg N/A

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

      3. neg-sub0 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(0 - z\right)}\right)\right) \cdot x \]

   10. Applied egg-rr 55.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-20}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(y, x, 0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -1.0) t_0 (if (<= x 7.6e-20) (fma y x (- 0.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 7.6e-20) {
		tmp = fma(y, x, (0.0 - 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 <= -1.0)
		tmp = t_0;
	elseif (x <= 7.6e-20)
		tmp = fma(y, x, Float64(0.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 7.6e-20], N[(y * x + N[(0.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 7.5999999999999995e-20 < x

   1. Initial program 98.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + z, 0\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

      4. +-lowering-+.f64 99.0

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

   5. Simplified 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. +-lowering-+.f64 99.0

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

   7. Applied egg-rr 99.0%

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

   if -1 < x < 7.5999999999999995e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto x \cdot y + \color{blue}{\left(0 - z\right)} \]

      3. --lowering--.f64 99.7

         \[\leadsto x \cdot y + \color{blue}{\left(0 - z\right)} \]

   5. Simplified 99.7%

      \[\leadsto x \cdot y + \color{blue}{\left(0 - z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + \left(0 - z\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0 - z\right)} \]

      3. --lowering--.f64 99.7

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{0 - z}\right) \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0 - z\right)} \]
   8. Step-by-step derivation

      1. flip3-- N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{\color{blue}{0} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}}\right) \]

      4. sqr-pow N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      5. pow-prod-down N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      6. sqr-neg N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\left(\color{blue}{\left(0 - z\right)} \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      8. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\left(\left(0 - z\right) \cdot \color{blue}{\left(0 - z\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      9. pow-prod-down N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      10. sqr-pow N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(0 - z\right)}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      12. cube-neg N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{\mathsf{neg}\left({z}^{3}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      13. sub0-neg N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{0 - {z}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{0}^{3}} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right) \]

      15. flip3-- N/A

          \[\leadsto \mathsf{fma}\left(y, x, \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \color{blue}{\left(0 - z\right)}\right) \]

   9. Applied egg-rr 99.7%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(y, x, 0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z + y\right) \cdot x\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ z y) x)))
   (if (<= x -3.1e-76) t_0 (if (<= x 1.4e-83) (- 0.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z + y) * x;
	double tmp;
	if (x <= -3.1e-76) {
		tmp = t_0;
	} else if (x <= 1.4e-83) {
		tmp = 0.0 - 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 <= (-3.1d-76)) then
        tmp = t_0
    else if (x <= 1.4d-83) then
        tmp = 0.0d0 - 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 <= -3.1e-76) {
		tmp = t_0;
	} else if (x <= 1.4e-83) {
		tmp = 0.0 - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z + y) * x
	tmp = 0
	if x <= -3.1e-76:
		tmp = t_0
	elif x <= 1.4e-83:
		tmp = 0.0 - 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 <= -3.1e-76)
		tmp = t_0;
	elseif (x <= 1.4e-83)
		tmp = Float64(0.0 - 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 <= -3.1e-76)
		tmp = t_0;
	elseif (x <= 1.4e-83)
		tmp = 0.0 - 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, -3.1e-76], t$95$0, If[LessEqual[x, 1.4e-83], N[(0.0 - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999997e-76 or 1.4e-83 < x

   1. Initial program 98.3%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + 0} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + z, 0\right)} \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

      4. +-lowering-+.f64 93.4

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{z + y}, 0\right) \]

   5. Simplified 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. +-lowering-+.f64 93.4

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

   7. Applied egg-rr 93.4%

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

   if -3.0999999999999997e-76 < x < 1.4e-83

   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-sub0 N/A

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

      3. --lowering--.f64 73.4

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

   5. Simplified 73.4%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 73.4

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

   7. Applied egg-rr 73.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e-19) (* y x) (if (<= y 1.15e+83) (* z (+ x -1.0)) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e-19) {
		tmp = y * x;
	} else if (y <= 1.15e+83) {
		tmp = z * (x + -1.0);
	} 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 (y <= (-1.3d-19)) then
        tmp = y * x
    else if (y <= 1.15d+83) then
        tmp = z * (x + (-1.0d0))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e-19) {
		tmp = y * x;
	} else if (y <= 1.15e+83) {
		tmp = z * (x + -1.0);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e-19:
		tmp = y * x
	elif y <= 1.15e+83:
		tmp = z * (x + -1.0)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e-19)
		tmp = Float64(y * x);
	elseif (y <= 1.15e+83)
		tmp = Float64(z * Float64(x + -1.0));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e-19)
		tmp = y * x;
	elseif (y <= 1.15e+83)
		tmp = z * (x + -1.0);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e-19], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.15e+83], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000006e-19 or 1.14999999999999997e83 < y

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot y + 0} \]

      2. accelerator-lowering-fma.f64 76.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 76.0

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

   7. Applied egg-rr 76.0%

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

   if -1.30000000000000006e-19 < y < 1.14999999999999997e83

   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. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. *-rgt-identity N/A

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

      5. *-inverses N/A

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

      6. associate-/l* N/A

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

      7. associate-*l/ N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. distribute-lft-neg-in N/A

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

      11. *-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. associate-+r- N/A

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + y, 0\right) - z} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

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

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

      4. +-lowering-+.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 80.3%

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

       1. sub-neg N/A

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

       2. *-commutative N/A

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

       3. neg-mul-1 N/A

          \[\leadsto x \cdot z + \color{blue}{-1 \cdot z} \]

       4. distribute-rgt-out N/A

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

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

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

       6. +-lowering-+.f64 80.3

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

   12. Applied egg-rr 80.3%

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

Alternative 6: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e-9) (* y x) (if (<= x 1.55e-83) (- 0.0 z) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-9) {
		tmp = y * x;
	} else if (x <= 1.55e-83) {
		tmp = 0.0 - 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 <= (-2.4d-9)) then
        tmp = y * x
    else if (x <= 1.55d-83) then
        tmp = 0.0d0 - 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 <= -2.4e-9) {
		tmp = y * x;
	} else if (x <= 1.55e-83) {
		tmp = 0.0 - z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e-9:
		tmp = y * x
	elif x <= 1.55e-83:
		tmp = 0.0 - z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e-9)
		tmp = Float64(y * x);
	elseif (x <= 1.55e-83)
		tmp = Float64(0.0 - z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e-9)
		tmp = y * x;
	elseif (x <= 1.55e-83)
		tmp = 0.0 - z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e-9], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.55e-83], N[(0.0 - z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e-9 or 1.54999999999999996e-83 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot y + 0} \]

      2. accelerator-lowering-fma.f64 55.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 55.4

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

   7. Applied egg-rr 55.4%

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

   if -2.4e-9 < x < 1.54999999999999996e-83

   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-sub0 N/A

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

      3. --lowering--.f64 69.5

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

   5. Simplified 69.5%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 69.5

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-83}:\\ \;\;\;\;0 - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 0.0 - 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 = 0.0d0 - z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(0.0 - z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(0.0 - z), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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-sub0 N/A

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

   3. --lowering--.f64 28.0

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

5. Simplified 28.0%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 28.0

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

7. Applied egg-rr 28.0%

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

8. Final simplification 28.0%

   \[\leadsto 0 - z \]
9. Add Preprocessing

Alternative 8: 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 98.8%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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-sub0 N/A

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

   3. --lowering--.f64 28.0

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

5. Simplified 28.0%

   \[\leadsto \color{blue}{0 - z} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 28.0

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

7. Applied egg-rr 28.0%

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

   1. neg-sub0 N/A

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

   2. flip3-- N/A

      \[\leadsto \color{blue}{\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}} \]

   3. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{0} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   4. div-sub N/A

      \[\leadsto \color{blue}{\frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}} \]

   5. sqr-pow N/A

      \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   6. pow-prod-down N/A

      \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   7. sqr-neg N/A

      \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   8. neg-sub0 N/A

      \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\left(\color{blue}{\left(0 - z\right)} \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   9. neg-sub0 N/A

      \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\left(\left(0 - z\right) \cdot \color{blue}{\left(0 - z\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   10. pow-prod-down N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   11. sqr-pow N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{\left(0 - z\right)}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   12. neg-sub0 N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{{\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   13. cube-neg N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{\mathsf{neg}\left({z}^{3}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   14. sub0-neg N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{0 - {z}^{3}}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   15. metadata-eval N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \frac{\color{blue}{{0}^{3}} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} \]

   16. flip3-- N/A

       \[\leadsto \frac{0}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - \color{blue}{\left(0 - z\right)} \]

9. Applied egg-rr 2.7%

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

Reproduce

herbie shell --seed 2024195 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))