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

Percentage Accurate: 98.0% → 100.0%

Time: 5.3s

Alternatives: 6

Speedup: 1.4×

• 20.7% 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: 98.0% 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 97.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 100.0%

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

Alternative 2: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-34}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-62}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+158)
   (* x z)
   (if (<= x -9.2e-34)
     (* y x)
     (if (<= x 5.8e-62) (- z) (if (<= x 2.6e+63) (* y x) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+158) {
		tmp = x * z;
	} else if (x <= -9.2e-34) {
		tmp = y * x;
	} else if (x <= 5.8e-62) {
		tmp = -z;
	} else if (x <= 2.6e+63) {
		tmp = y * x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d+158)) then
        tmp = x * z
    else if (x <= (-9.2d-34)) then
        tmp = y * x
    else if (x <= 5.8d-62) then
        tmp = -z
    else if (x <= 2.6d+63) then
        tmp = y * x
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+158) {
		tmp = x * z;
	} else if (x <= -9.2e-34) {
		tmp = y * x;
	} else if (x <= 5.8e-62) {
		tmp = -z;
	} else if (x <= 2.6e+63) {
		tmp = y * x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+158:
		tmp = x * z
	elif x <= -9.2e-34:
		tmp = y * x
	elif x <= 5.8e-62:
		tmp = -z
	elif x <= 2.6e+63:
		tmp = y * x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+158)
		tmp = Float64(x * z);
	elseif (x <= -9.2e-34)
		tmp = Float64(y * x);
	elseif (x <= 5.8e-62)
		tmp = Float64(-z);
	elseif (x <= 2.6e+63)
		tmp = Float64(y * x);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+158)
		tmp = x * z;
	elseif (x <= -9.2e-34)
		tmp = y * x;
	elseif (x <= 5.8e-62)
		tmp = -z;
	elseif (x <= 2.6e+63)
		tmp = y * x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+158], N[(x * z), $MachinePrecision], If[LessEqual[x, -9.2e-34], N[(y * x), $MachinePrecision], If[LessEqual[x, 5.8e-62], (-z), If[LessEqual[x, 2.6e+63], N[(y * x), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e158 or 2.6000000000000001e63 < x

   1. Initial program 90.7%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. *-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 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 92.3%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 65.1%

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

   if -2.0999999999999999e158 < x < -9.20000000000000045e-34 or 5.79999999999999971e-62 < x < 2.6000000000000001e63

   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 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 88.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 23.9%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 66.4

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

   13. Applied rewrites 66.4%

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

   if -9.20000000000000045e-34 < x < 5.79999999999999971e-62

   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 73.2

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

   5. Applied rewrites 73.2%

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

Alternative 3: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -70000 \lor \neg \left(x \leq 4.2 \cdot 10^{-44}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -70000.0) (not (<= x 4.2e-44))) (* (+ z y) x) (* (+ -1.0 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -70000.0) || !(x <= 4.2e-44)) {
		tmp = (z + y) * x;
	} else {
		tmp = (-1.0 + x) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-70000.0d0)) .or. (.not. (x <= 4.2d-44))) then
        tmp = (z + y) * x
    else
        tmp = ((-1.0d0) + x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -70000.0) || !(x <= 4.2e-44)) {
		tmp = (z + y) * x;
	} else {
		tmp = (-1.0 + x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -70000.0) or not (x <= 4.2e-44):
		tmp = (z + y) * x
	else:
		tmp = (-1.0 + x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -70000.0) || !(x <= 4.2e-44))
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = Float64(Float64(-1.0 + x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -70000.0) || ~((x <= 4.2e-44)))
		tmp = (z + y) * x;
	else
		tmp = (-1.0 + x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -70000.0], N[Not[LessEqual[x, 4.2e-44]], $MachinePrecision]], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], N[(N[(-1.0 + x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e4 or 4.20000000000000003e-44 < x

   1. Initial program 94.9%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 97.7

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

   5. Applied rewrites 97.7%

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

   if -7e4 < x < 4.20000000000000003e-44

   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. 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 72.2

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

   5. Applied rewrites 72.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -70000 \lor \neg \left(x \leq 4.2 \cdot 10^{-44}\right):\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-129} \lor \neg \left(z \leq 1.5 \cdot 10^{-108}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e-129) (not (<= z 1.5e-108))) (* (+ -1.0 x) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e-129) || !(z <= 1.5e-108)) {
		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 <= (-7.5d-129)) .or. (.not. (z <= 1.5d-108))) 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 <= -7.5e-129) || !(z <= 1.5e-108)) {
		tmp = (-1.0 + x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e-129) or not (z <= 1.5e-108):
		tmp = (-1.0 + x) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e-129) || !(z <= 1.5e-108))
		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 <= -7.5e-129) || ~((z <= 1.5e-108)))
		tmp = (-1.0 + x) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e-129], N[Not[LessEqual[z, 1.5e-108]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999944e-129 or 1.49999999999999996e-108 < z

   1. Initial program 96.4%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 81.9

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

   5. Applied rewrites 81.9%

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

   if -7.49999999999999944e-129 < z < 1.49999999999999996e-108

   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 83.3

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

   5. Applied rewrites 83.3%

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 9.0%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 75.1

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

   13. Applied rewrites 75.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-129} \lor \neg \left(z \leq 1.5 \cdot 10^{-108}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+26} \lor \neg \left(x \leq 9.2 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.1e+26) (not (<= x 9.2e-11))) (* x z) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e+26) || !(x <= 9.2e-11)) {
		tmp = x * z;
	} 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 <= (-6.1d+26)) .or. (.not. (x <= 9.2d-11))) then
        tmp = x * z
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e+26) || !(x <= 9.2e-11)) {
		tmp = x * z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.1e+26) or not (x <= 9.2e-11):
		tmp = x * z
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.1e+26) || !(x <= 9.2e-11))
		tmp = Float64(x * z);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.1e+26) || ~((x <= 9.2e-11)))
		tmp = x * z;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.1e+26], N[Not[LessEqual[x, 9.2e-11]], $MachinePrecision]], N[(x * z), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -6.1000000000000003e26 or 9.20000000000000054e-11 < x

   1. Initial program 94.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 95.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 51.6%

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

   if -6.1000000000000003e26 < x < 9.20000000000000054e-11

   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 68.1

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

   5. Applied rewrites 68.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+26} \lor \neg \left(x \leq 9.2 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.6% 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 97.6%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
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 40.2

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

5. Applied rewrites 40.2%

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

Reproduce

herbie shell --seed 2024342 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))