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

Percentage Accurate: 98.0% → 99.0%

Time: 6.5s

Alternatives: 9

Speedup: 1.1×

• 21.3% 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: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, \left(x + -1\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y x (* (+ x -1.0) z)))

C

double code(double x, double y, double z) {
	return fma(y, x, ((x + -1.0) * z));
}

Julia

function code(x, y, z)
	return fma(y, x, Float64(Float64(x + -1.0) * z))
end

Wolfram

code[x_, y_, z_] := N[(y * x + N[(N[(x + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 100.0

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

   5. lift--.f64 N/A

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

   6. sub-neg N/A

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

   7. lower-+.f64 N/A

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

   8. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+201}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e-13)
   (* y x)
   (if (<= x 1.0) (- z) (if (<= x 1.85e+201) (* x z) (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-13) {
		tmp = y * x;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 1.85e+201) {
		tmp = 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 (x <= (-1.75d-13)) then
        tmp = y * x
    else if (x <= 1.0d0) then
        tmp = -z
    else if (x <= 1.85d+201) then
        tmp = 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 (x <= -1.75e-13) {
		tmp = y * x;
	} else if (x <= 1.0) {
		tmp = -z;
	} else if (x <= 1.85e+201) {
		tmp = x * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-13:
		tmp = y * x
	elif x <= 1.0:
		tmp = -z
	elif x <= 1.85e+201:
		tmp = x * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-13)
		tmp = Float64(y * x);
	elseif (x <= 1.0)
		tmp = Float64(-z);
	elseif (x <= 1.85e+201)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-13)
		tmp = y * x;
	elseif (x <= 1.0)
		tmp = -z;
	elseif (x <= 1.85e+201)
		tmp = x * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-13], N[(y * x), $MachinePrecision], If[LessEqual[x, 1.0], (-z), If[LessEqual[x, 1.85e+201], N[(x * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e-13 or 1.8499999999999999e201 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 63.2

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

   5. Applied rewrites 63.2%

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

   if -1.7500000000000001e-13 < 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 73.5

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

   5. Applied rewrites 73.5%

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

   if 1 < x < 1.8499999999999999e201

   1. Initial program 97.3%

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

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 68.5

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 65.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+201}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, x, x \cdot z\right)\\ \mathbf{if}\;x \leq -110000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma y x (* x z))))
   (if (<= x -110000.0) t_0 (if (<= x 1.0) (fma y x (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(y, x, (x * z));
	double tmp;
	if (x <= -110000.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = fma(y, x, -z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(y, x, Float64(x * z))
	tmp = 0.0
	if (x <= -110000.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = fma(y, x, Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -110000.0], t$95$0, If[LessEqual[x, 1.0], N[(y * x + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e5 or 1 < x

   1. Initial program 98.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. lower-+.f64 N/A

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

      8. metadata-eval 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.7

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

   7. Applied rewrites 98.7%

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

   if -1.1e5 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. lower-+.f64 N/A

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

      8. metadata-eval 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.0

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

   7. Applied rewrites 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -110000:\\ \;\;\;\;\mathsf{fma}\left(y, x, x \cdot z\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -110000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -110000.0) t_0 (if (<= x 1.0) (fma y x (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -110000.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = fma(y, x, -z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -110000.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = fma(y, x, Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -110000.0], t$95$0, If[LessEqual[x, 1.0], N[(y * x + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e5 or 1 < x

   1. Initial program 98.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. lower-*.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. lower-+.f64 98.7

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

   5. Applied rewrites 98.7%

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

   if -1.1e5 < x < 1

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. lower-+.f64 N/A

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

      8. metadata-eval 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.0

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

   7. Applied rewrites 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -110000:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(y, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 32000000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.75e-13) t_0 (if (<= x 32000000000000.0) (fma z x (- z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.75e-13) {
		tmp = t_0;
	} else if (x <= 32000000000000.0) {
		tmp = fma(z, x, -z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.75e-13)
		tmp = t_0;
	elseif (x <= 32000000000000.0)
		tmp = fma(z, x, Float64(-z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e-13], t$95$0, If[LessEqual[x, 32000000000000.0], N[(z * x + (-z)), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-13 or 3.2e13 < x

   1. Initial program 98.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   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. lower-*.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. lower-+.f64 99.6

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

   5. Applied rewrites 99.6%

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

   if -1.7500000000000001e-13 < x < 3.2e13

   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. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 75.0

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

   5. Applied rewrites 75.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 32000000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-9}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.75e-13) t_0 (if (<= x 8.6e-9) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.75e-13) {
		tmp = t_0;
	} else if (x <= 8.6e-9) {
		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 * (y + z)
    if (x <= (-1.75d-13)) then
        tmp = t_0
    else if (x <= 8.6d-9) 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 * (y + z);
	double tmp;
	if (x <= -1.75e-13) {
		tmp = t_0;
	} else if (x <= 8.6e-9) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.75e-13:
		tmp = t_0
	elif x <= 8.6e-9:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.75e-13)
		tmp = t_0;
	elseif (x <= 8.6e-9)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1.75e-13)
		tmp = t_0;
	elseif (x <= 8.6e-9)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e-13], t$95$0, If[LessEqual[x, 8.6e-9], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-13 or 8.59999999999999925e-9 < 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. lower-*.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. lower-+.f64 98.7

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

   5. Applied rewrites 98.7%

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

   if -1.7500000000000001e-13 < x < 8.59999999999999925e-9

   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 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-9}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.7e-11) (* x z) (if (<= x 1.0) (- z) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.7e-11) {
		tmp = x * z;
	} else if (x <= 1.0) {
		tmp = -z;
	} 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 <= (-9.7d-11)) then
        tmp = x * z
    else if (x <= 1.0d0) then
        tmp = -z
    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 <= -9.7e-11) {
		tmp = x * z;
	} else if (x <= 1.0) {
		tmp = -z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.7e-11:
		tmp = x * z
	elif x <= 1.0:
		tmp = -z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.7e-11)
		tmp = Float64(x * z);
	elseif (x <= 1.0)
		tmp = Float64(-z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.7e-11)
		tmp = x * z;
	elseif (x <= 1.0)
		tmp = -z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.7e-11], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.0], (-z), N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.7000000000000001e-11 or 1 < x

   1. Initial program 98.3%

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

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 53.5

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

   5. Applied rewrites 53.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 52.3%

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

   if -9.7000000000000001e-11 < 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 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.0% 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 99.2%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 41.1

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

5. Applied rewrites 41.1%

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

Alternative 9: 2.5% 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 99.2%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 41.1

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

5. Applied rewrites 41.1%

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

7. Applied rewrites 2.5%

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

Reproduce

herbie shell --seed 2024238 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))