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

Percentage Accurate: 97.8% → 100.0%

Time: 4.0s

Alternatives: 5

Speedup: 1.3×

• 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, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. distribute-rgt-out-- 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. metadata-eval 98.0%

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

   5. neg-mul-1 98.0%

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

   6. associate-+r+ 98.0%

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

   7. unsub-neg 98.0%

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

   8. +-commutative 98.0%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-178} \lor \neg \left(y \leq 2.2 \cdot 10^{-127}\right):\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e-178) (not (<= y 2.2e-127))) (- (* x y) z) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e-178) || !(y <= 2.2e-127)) {
		tmp = (x * y) - z;
	} else {
		tmp = (x * z) - 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 ((y <= (-3.8d-178)) .or. (.not. (y <= 2.2d-127))) then
        tmp = (x * y) - z
    else
        tmp = (x * z) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e-178) || !(y <= 2.2e-127)) {
		tmp = (x * y) - z;
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e-178) or not (y <= 2.2e-127):
		tmp = (x * y) - z
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e-178) || !(y <= 2.2e-127))
		tmp = Float64(Float64(x * y) - z);
	else
		tmp = Float64(Float64(x * z) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e-178) || ~((y <= 2.2e-127)))
		tmp = (x * y) - z;
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e-178], N[Not[LessEqual[y, 2.2e-127]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000015e-178 or 2.2000000000000001e-127 < y

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. distribute-rgt-out-- 97.4%

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

      3. cancel-sign-sub-inv 97.4%

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

      4. metadata-eval 97.4%

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

      5. neg-mul-1 97.4%

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

      6. associate-+r+ 97.4%

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

      7. unsub-neg 97.4%

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

      8. +-commutative 97.4%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.9%

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

   if -3.80000000000000015e-178 < y < 2.2000000000000001e-127

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-rgt-out-- 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 94.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-178} \lor \neg \left(y \leq 2.2 \cdot 10^{-127}\right):\\ \;\;\;\;x \cdot y - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+32} \lor \neg \left(x \leq 6.5 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e+32) (not (<= x 6.5e-5))) (* x z) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e+32) || !(x <= 6.5e-5)) {
		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 <= (-1.65d+32)) .or. (.not. (x <= 6.5d-5))) 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 <= -1.65e+32) || !(x <= 6.5e-5)) {
		tmp = x * z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e+32) or not (x <= 6.5e-5):
		tmp = x * z
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e+32) || !(x <= 6.5e-5))
		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 <= -1.65e+32) || ~((x <= 6.5e-5)))
		tmp = x * z;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e+32], N[Not[LessEqual[x, 6.5e-5]], $MachinePrecision]], N[(x * z), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.6500000000000001e32 or 6.49999999999999943e-5 < x

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. distribute-rgt-out-- 95.5%

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

      3. cancel-sign-sub-inv 95.5%

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

      4. metadata-eval 95.5%

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

      5. neg-mul-1 95.5%

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

      6. associate-+r+ 95.5%

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

      7. unsub-neg 95.5%

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

      8. +-commutative 95.5%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 53.2%

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

   6. Taylor expanded in x around inf 53.1%

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

      1. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -1.6500000000000001e32 < x < 6.49999999999999943e-5

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 68.8%

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

      1. mul-1-neg 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+32} \lor \neg \left(x \leq 6.5 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot y - z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. distribute-rgt-out-- 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. metadata-eval 98.0%

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

   5. neg-mul-1 98.0%

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

   6. associate-+r+ 98.0%

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

   7. unsub-neg 98.0%

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

   8. +-commutative 98.0%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around 0 79.1%

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

Alternative 5: 37.3% accurate, 4.5× 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 98.0%

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

   1. fma-define 99.6%

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

   2. sub-neg 99.6%

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

   3. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 40.2%

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

   1. mul-1-neg 40.2%

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

7. Simplified 40.2%

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))