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

Percentage Accurate: 97.8% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.4×

• 20.8% 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

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

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 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-57}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+139}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0)
   (* z x)
   (if (<= x 7.5e-57) (- z) (if (<= x 1.45e+139) (* y x) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = z * x;
	} else if (x <= 7.5e-57) {
		tmp = -z;
	} else if (x <= 1.45e+139) {
		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 <= (-1.0d0)) then
        tmp = z * x
    else if (x <= 7.5d-57) then
        tmp = -z
    else if (x <= 1.45d+139) 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 <= -1.0) {
		tmp = z * x;
	} else if (x <= 7.5e-57) {
		tmp = -z;
	} else if (x <= 1.45e+139) {
		tmp = y * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = z * x
	elif x <= 7.5e-57:
		tmp = -z
	elif x <= 1.45e+139:
		tmp = y * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(z * x);
	elseif (x <= 7.5e-57)
		tmp = Float64(-z);
	elseif (x <= 1.45e+139)
		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 <= -1.0)
		tmp = z * x;
	elseif (x <= 7.5e-57)
		tmp = -z;
	elseif (x <= 1.45e+139)
		tmp = y * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 7.5e-57], (-z), If[LessEqual[x, 1.45e+139], N[(y * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 1.4499999999999999e139 < x

   1. Initial program 96.2%

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

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 63.8%

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

   if -1 < x < 7.49999999999999973e-57

   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 69.3

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

   5. Applied rewrites 69.3%

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

   if 7.49999999999999973e-57 < x < 1.4499999999999999e139

   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 13.1

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

   5. Applied rewrites 13.1%

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

   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 54.9

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

   8. Applied rewrites 54.9%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-45) (not (<= z 2.25e-68))) (fma z x (- z)) (* (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-45) || !(z <= 2.25e-68)) {
		tmp = fma(z, x, -z);
	} else {
		tmp = (z + y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-45) || !(z <= 2.25e-68))
		tmp = fma(z, x, Float64(-z));
	else
		tmp = Float64(Float64(z + y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-45], N[Not[LessEqual[z, 2.25e-68]], $MachinePrecision]], N[(z * x + (-z)), $MachinePrecision], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000011e-45 or 2.25e-68 < z

   1. Initial program 97.5%

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

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 86.5

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

   5. Applied rewrites 86.5%

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

   7. Applied rewrites 86.5%

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

   if -3.00000000000000011e-45 < z < 2.25e-68

   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. *-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 86.9

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

   5. Applied rewrites 86.9%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-45) (not (<= z 2.25e-68))) (* (+ -1.0 x) z) (* (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-45) || !(z <= 2.25e-68)) {
		tmp = (-1.0 + x) * z;
	} else {
		tmp = (z + 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 ((z <= (-3d-45)) .or. (.not. (z <= 2.25d-68))) then
        tmp = ((-1.0d0) + x) * z
    else
        tmp = (z + y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-45) || !(z <= 2.25e-68)) {
		tmp = (-1.0 + x) * z;
	} else {
		tmp = (z + y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-45) or not (z <= 2.25e-68):
		tmp = (-1.0 + x) * z
	else:
		tmp = (z + y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-45) || !(z <= 2.25e-68))
		tmp = Float64(Float64(-1.0 + x) * z);
	else
		tmp = Float64(Float64(z + y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-45) || ~((z <= 2.25e-68)))
		tmp = (-1.0 + x) * z;
	else
		tmp = (z + y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-45], N[Not[LessEqual[z, 2.25e-68]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * z), $MachinePrecision], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000011e-45 or 2.25e-68 < z

   1. Initial program 97.5%

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

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -3.00000000000000011e-45 < z < 2.25e-68

   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. *-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 86.9

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

   5. Applied rewrites 86.9%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-55) (not (<= z 2.25e-68))) (* (+ -1.0 x) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-55) || !(z <= 2.25e-68)) {
		tmp = (-1.0 + x) * 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 ((z <= (-3.5d-55)) .or. (.not. (z <= 2.25d-68))) then
        tmp = ((-1.0d0) + x) * 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 ((z <= -3.5e-55) || !(z <= 2.25e-68)) {
		tmp = (-1.0 + x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-55) or not (z <= 2.25e-68):
		tmp = (-1.0 + x) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e-55) || !(z <= 2.25e-68))
		tmp = Float64(Float64(-1.0 + x) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e-55) || ~((z <= 2.25e-68)))
		tmp = (-1.0 + x) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-55], N[Not[LessEqual[z, 2.25e-68]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000025e-55 or 2.25e-68 < z

   1. Initial program 97.6%

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

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 86.1

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

   5. Applied rewrites 86.1%

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

   if -3.50000000000000025e-55 < z < 2.25e-68

   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 15.9

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

   5. Applied rewrites 15.9%

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

   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 78.6

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

   8. Applied rewrites 78.6%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (* z x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = 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 <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = 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 <= -1.0) || !(x <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = z * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(z * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = z * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 97.1%

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

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-out N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 60.9

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

   5. Applied rewrites 60.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 59.8%

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

   if -1 < 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 67.0

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

   5. Applied rewrites 67.0%

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

4. Final simplification 63.2%

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

Alternative 7: 37.1% 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 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 33.2

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

5. Applied rewrites 33.2%

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

Reproduce

herbie shell --seed 2024320 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))