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

Percentage Accurate: 98.1% → 100.0%

Time: 3.3s

Alternatives: 7

Speedup: 1.3×

• 20.4% 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: 98.1% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. *-commutative 96.9%

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

   2. sub-neg 96.9%

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

   3. distribute-rgt-in 96.9%

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

   4. associate-+r+ 96.9%

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

   5. distribute-lft-out 100.0%

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

   6. fma-def 100.0%

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

   7. metadata-eval 100.0%

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

   8. mul-1-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6300000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+58} \lor \neg \left(x \leq 4.1 \cdot 10^{+121}\right) \land x \leq 6.2 \cdot 10^{+214}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e-7)
   (* x z)
   (if (<= x 3.7e-100)
     (- z)
     (if (<= x 6300000000000.0)
       (* x y)
       (if (or (<= x 8.8e+58) (and (not (<= x 4.1e+121)) (<= x 6.2e+214)))
         (* x z)
         (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-7) {
		tmp = x * z;
	} else if (x <= 3.7e-100) {
		tmp = -z;
	} else if (x <= 6300000000000.0) {
		tmp = x * y;
	} else if ((x <= 8.8e+58) || (!(x <= 4.1e+121) && (x <= 6.2e+214))) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	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 <= (-1d-7)) then
        tmp = x * z
    else if (x <= 3.7d-100) then
        tmp = -z
    else if (x <= 6300000000000.0d0) then
        tmp = x * y
    else if ((x <= 8.8d+58) .or. (.not. (x <= 4.1d+121)) .and. (x <= 6.2d+214)) then
        tmp = x * z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-7) {
		tmp = x * z;
	} else if (x <= 3.7e-100) {
		tmp = -z;
	} else if (x <= 6300000000000.0) {
		tmp = x * y;
	} else if ((x <= 8.8e+58) || (!(x <= 4.1e+121) && (x <= 6.2e+214))) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e-7:
		tmp = x * z
	elif x <= 3.7e-100:
		tmp = -z
	elif x <= 6300000000000.0:
		tmp = x * y
	elif (x <= 8.8e+58) or (not (x <= 4.1e+121) and (x <= 6.2e+214)):
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e-7)
		tmp = Float64(x * z);
	elseif (x <= 3.7e-100)
		tmp = Float64(-z);
	elseif (x <= 6300000000000.0)
		tmp = Float64(x * y);
	elseif ((x <= 8.8e+58) || (!(x <= 4.1e+121) && (x <= 6.2e+214)))
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e-7)
		tmp = x * z;
	elseif (x <= 3.7e-100)
		tmp = -z;
	elseif (x <= 6300000000000.0)
		tmp = x * y;
	elseif ((x <= 8.8e+58) || (~((x <= 4.1e+121)) && (x <= 6.2e+214)))
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e-7], N[(x * z), $MachinePrecision], If[LessEqual[x, 3.7e-100], (-z), If[LessEqual[x, 6300000000000.0], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 8.8e+58], And[N[Not[LessEqual[x, 4.1e+121]], $MachinePrecision], LessEqual[x, 6.2e+214]]], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999995e-8 or 6.3e12 < x < 8.8000000000000003e58 or 4.1e121 < x < 6.19999999999999957e214

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

      2. sub-neg 93.7%

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

      3. distribute-rgt-in 93.7%

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

      4. associate-+r+ 93.7%

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

      5. metadata-eval 93.7%

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

      6. mul-1-neg 93.7%

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

      7. unsub-neg 93.7%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 63.8%

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

   5. Taylor expanded in x around inf 63.9%

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

   if -9.9999999999999995e-8 < x < 3.70000000000000018e-100

   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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

   6. Simplified 72.7%

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

   if 3.70000000000000018e-100 < x < 6.3e12 or 8.8000000000000003e58 < x < 4.1e121 or 6.19999999999999957e214 < x

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. sub-neg 95.3%

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

      3. distribute-rgt-in 95.3%

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

      4. associate-+r+ 95.3%

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

      5. metadata-eval 95.3%

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

      6. mul-1-neg 95.3%

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

      7. unsub-neg 95.3%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 79.4%

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

   5. Taylor expanded in y around inf 67.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 6300000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+58} \lor \neg \left(x \leq 4.1 \cdot 10^{+121}\right) \land x \leq 6.2 \cdot 10^{+214}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-11} \lor \neg \left(x \leq 4 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-11) (not (<= x 4e-100))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-11) || !(x <= 4e-100)) {
		tmp = x * (y + 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-11)) .or. (.not. (x <= 4d-100))) then
        tmp = x * (y + 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-11) || !(x <= 4e-100)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-11) or not (x <= 4e-100):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-11) || !(x <= 4e-100))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.65e-11) || ~((x <= 4e-100)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-11], N[Not[LessEqual[x, 4e-100]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.6500000000000001e-11 or 4.0000000000000001e-100 < x

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. sub-neg 94.4%

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

      3. distribute-rgt-in 94.4%

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

      4. associate-+r+ 94.4%

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

      5. metadata-eval 94.4%

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

      6. mul-1-neg 94.4%

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

      7. unsub-neg 94.4%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.4%

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

      3. associate-+l+ 94.4%

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

      4. neg-mul-1 94.4%

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

      5. distribute-rgt-in 94.4%

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

      6. *-commutative 94.4%

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

      7. +-commutative 94.4%

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

      8. fma-def 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in x around inf 93.6%

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

   if -1.6500000000000001e-11 < x < 4.0000000000000001e-100

   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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-11} \lor \neg \left(x \leq 4 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 98.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = x * (y + z);
	else
		tmp = (x * y) - 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[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

      2. sub-neg 93.3%

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

      3. distribute-rgt-in 93.3%

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

      4. associate-+r+ 93.3%

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

      5. metadata-eval 93.3%

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

      6. mul-1-neg 93.3%

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

      7. unsub-neg 93.3%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.3%

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

      3. associate-+l+ 93.3%

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

      4. neg-mul-1 93.3%

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

      5. distribute-rgt-in 93.3%

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

      6. *-commutative 93.3%

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

      7. +-commutative 93.3%

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

      8. fma-def 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in x around inf 99.5%

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

   if -1 < x < 1

   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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.3%

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

4. Final simplification 99.4%

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

Alternative 5: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-103}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-11) (* x y) (if (<= x 4.3e-103) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-11) {
		tmp = x * y;
	} else if (x <= 4.3e-103) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	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 <= (-1.45d-11)) then
        tmp = x * y
    else if (x <= 4.3d-103) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-11) {
		tmp = x * y;
	} else if (x <= 4.3e-103) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-11:
		tmp = x * y
	elif x <= 4.3e-103:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-11)
		tmp = Float64(x * y);
	elseif (x <= 4.3e-103)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e-11)
		tmp = x * y;
	elseif (x <= 4.3e-103)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.3e-103], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e-11 or 4.30000000000000023e-103 < x

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. sub-neg 94.4%

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

      3. distribute-rgt-in 94.4%

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

      4. associate-+r+ 94.4%

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

      5. metadata-eval 94.4%

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

      6. mul-1-neg 94.4%

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

      7. unsub-neg 94.4%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 57.2%

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

   5. Taylor expanded in y around inf 51.5%

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

   if -1.45e-11 < x < 4.30000000000000023e-103

   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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. mul-1-neg 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-103}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. *-commutative 96.9%

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

   2. sub-neg 96.9%

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

   3. distribute-rgt-in 96.9%

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

   4. associate-+r+ 96.9%

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

   5. metadata-eval 96.9%

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

   6. mul-1-neg 96.9%

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

   7. unsub-neg 96.9%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 7: 36.9% 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 96.9%

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

   1. *-commutative 96.9%

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

   2. sub-neg 96.9%

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

   3. distribute-rgt-in 96.9%

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

   4. associate-+r+ 96.9%

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

   5. metadata-eval 96.9%

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

   6. mul-1-neg 96.9%

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

   7. unsub-neg 96.9%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 36.4%

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

   1. mul-1-neg 36.4%

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

6. Simplified 36.4%

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

7. Final simplification 36.4%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))