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

Percentage Accurate: 98.0% → 100.0%

Time: 6.9s

Alternatives: 8

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: 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. sub-neg 97.2%

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

   3. distribute-rgt-in 97.2%

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

   4. metadata-eval 97.2%

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

   5. neg-mul-1 97.2%

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

   6. associate-+r+ 97.2%

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

   7. distribute-lft-in 99.9%

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

   8. *-commutative 99.9%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+98} \lor \neg \left(x \leq 6.2 \cdot 10^{+112}\right) \land \left(x \leq 5.6 \cdot 10^{+169} \lor \neg \left(x \leq 4.2 \cdot 10^{+238}\right) \land x \leq 2.95 \cdot 10^{+258}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e+72)
   (* z x)
   (if (<= x -0.0066)
     (* y x)
     (if (<= x 4.7e-138)
       (- z)
       (if (<= x 5e+62)
         (* y x)
         (if (or (<= x 1.16e+98)
                 (and (not (<= x 6.2e+112))
                      (or (<= x 5.6e+169)
                          (and (not (<= x 4.2e+238)) (<= x 2.95e+258)))))
           (* z x)
           (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e+72) {
		tmp = z * x;
	} else if (x <= -0.0066) {
		tmp = y * x;
	} else if (x <= 4.7e-138) {
		tmp = -z;
	} else if (x <= 5e+62) {
		tmp = y * x;
	} else if ((x <= 1.16e+98) || (!(x <= 6.2e+112) && ((x <= 5.6e+169) || (!(x <= 4.2e+238) && (x <= 2.95e+258))))) {
		tmp = z * x;
	} 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 <= (-9.5d+72)) then
        tmp = z * x
    else if (x <= (-0.0066d0)) then
        tmp = y * x
    else if (x <= 4.7d-138) then
        tmp = -z
    else if (x <= 5d+62) then
        tmp = y * x
    else if ((x <= 1.16d+98) .or. (.not. (x <= 6.2d+112)) .and. (x <= 5.6d+169) .or. (.not. (x <= 4.2d+238)) .and. (x <= 2.95d+258)) then
        tmp = z * x
    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 <= -9.5e+72) {
		tmp = z * x;
	} else if (x <= -0.0066) {
		tmp = y * x;
	} else if (x <= 4.7e-138) {
		tmp = -z;
	} else if (x <= 5e+62) {
		tmp = y * x;
	} else if ((x <= 1.16e+98) || (!(x <= 6.2e+112) && ((x <= 5.6e+169) || (!(x <= 4.2e+238) && (x <= 2.95e+258))))) {
		tmp = z * x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e+72:
		tmp = z * x
	elif x <= -0.0066:
		tmp = y * x
	elif x <= 4.7e-138:
		tmp = -z
	elif x <= 5e+62:
		tmp = y * x
	elif (x <= 1.16e+98) or (not (x <= 6.2e+112) and ((x <= 5.6e+169) or (not (x <= 4.2e+238) and (x <= 2.95e+258)))):
		tmp = z * x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e+72)
		tmp = Float64(z * x);
	elseif (x <= -0.0066)
		tmp = Float64(y * x);
	elseif (x <= 4.7e-138)
		tmp = Float64(-z);
	elseif (x <= 5e+62)
		tmp = Float64(y * x);
	elseif ((x <= 1.16e+98) || (!(x <= 6.2e+112) && ((x <= 5.6e+169) || (!(x <= 4.2e+238) && (x <= 2.95e+258)))))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e+72)
		tmp = z * x;
	elseif (x <= -0.0066)
		tmp = y * x;
	elseif (x <= 4.7e-138)
		tmp = -z;
	elseif (x <= 5e+62)
		tmp = y * x;
	elseif ((x <= 1.16e+98) || (~((x <= 6.2e+112)) && ((x <= 5.6e+169) || (~((x <= 4.2e+238)) && (x <= 2.95e+258)))))
		tmp = z * x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e+72], N[(z * x), $MachinePrecision], If[LessEqual[x, -0.0066], N[(y * x), $MachinePrecision], If[LessEqual[x, 4.7e-138], (-z), If[LessEqual[x, 5e+62], N[(y * x), $MachinePrecision], If[Or[LessEqual[x, 1.16e+98], And[N[Not[LessEqual[x, 6.2e+112]], $MachinePrecision], Or[LessEqual[x, 5.6e+169], And[N[Not[LessEqual[x, 4.2e+238]], $MachinePrecision], LessEqual[x, 2.95e+258]]]]], N[(z * x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000054e72 or 5.00000000000000029e62 < x < 1.15999999999999995e98 or 6.19999999999999965e112 < x < 5.6000000000000003e169 or 4.20000000000000015e238 < x < 2.95e258

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 71.8%

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

   if -9.50000000000000054e72 < x < -0.0066 or 4.7000000000000001e-138 < x < 5.00000000000000029e62 or 1.15999999999999995e98 < x < 6.19999999999999965e112 or 5.6000000000000003e169 < x < 4.20000000000000015e238 or 2.95e258 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 69.0%

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

   if -0.0066 < x < 4.7000000000000001e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+98} \lor \neg \left(x \leq 6.2 \cdot 10^{+112}\right) \land \left(x \leq 5.6 \cdot 10^{+169} \lor \neg \left(x \leq 4.2 \cdot 10^{+238}\right) \land x \leq 2.95 \cdot 10^{+258}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0066) (not (<= x 5.1e-138))) (* (+ y z) x) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0066) || !(x <= 5.1e-138)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.0066d0)) .or. (.not. (x <= 5.1d-138))) then
        tmp = (y + z) * x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0066) || !(x <= 5.1e-138)) {
		tmp = (y + z) * x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0066) or not (x <= 5.1e-138):
		tmp = (y + z) * x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0066) || !(x <= 5.1e-138))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0066) || ~((x <= 5.1e-138)))
		tmp = (y + z) * x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0066], N[Not[LessEqual[x, 5.1e-138]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 5.1000000000000002e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -0.0066 < x < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.012 \lor \neg \left(x \leq 1.15 \cdot 10^{-140}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.012) (not (<= x 1.15e-140))) (* (+ y z) x) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.012) || !(x <= 1.15e-140)) {
		tmp = (y + z) * x;
	} else {
		tmp = z * (x + -1.0);
	}
	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) :: tmp
    if ((x <= (-0.012d0)) .or. (.not. (x <= 1.15d-140))) then
        tmp = (y + z) * x
    else
        tmp = z * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.012) || !(x <= 1.15e-140)) {
		tmp = (y + z) * x;
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.012) or not (x <= 1.15e-140):
		tmp = (y + z) * x
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.012) || !(x <= 1.15e-140))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(z * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.012) || ~((x <= 1.15e-140)))
		tmp = (y + z) * x;
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.012], N[Not[LessEqual[x, 1.15e-140]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.012 or 1.1500000000000001e-140 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -0.012 < x < 1.1500000000000001e-140

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.012 \lor \neg \left(x \leq 1.15 \cdot 10^{-140}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.024 \lor \neg \left(x \leq 4.2 \cdot 10^{-138}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.024) (not (<= x 4.2e-138))) (* (+ y z) x) (- (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.024) || !(x <= 4.2e-138)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * 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 <= (-0.024d0)) .or. (.not. (x <= 4.2d-138))) then
        tmp = (y + z) * x
    else
        tmp = (z * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.024) || !(x <= 4.2e-138)) {
		tmp = (y + z) * x;
	} else {
		tmp = (z * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.024) or not (x <= 4.2e-138):
		tmp = (y + z) * x
	else:
		tmp = (z * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.024) || !(x <= 4.2e-138))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(Float64(z * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.024) || ~((x <= 4.2e-138)))
		tmp = (y + z) * x;
	else
		tmp = (z * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.024], N[Not[LessEqual[x, 4.2e-138]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.024 or 4.19999999999999972e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -0.024 < x < 4.19999999999999972e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.8%

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

      1. sub-neg 79.8%

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

      2. metadata-eval 79.8%

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

      3. distribute-rgt-in 79.8%

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

      4. mul-1-neg 79.8%

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

      5. sub-neg 79.8%

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

      6. *-commutative 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.024 \lor \neg \left(x \leq 4.2 \cdot 10^{-138}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z\\ \end{array} \]

Alternative 6: 60.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0066) (* y x) (if (<= x 5.1e-138) (- z) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0066) {
		tmp = y * x;
	} else if (x <= 5.1e-138) {
		tmp = -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 <= (-0.0066d0)) then
        tmp = y * x
    else if (x <= 5.1d-138) then
        tmp = -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 <= -0.0066) {
		tmp = y * x;
	} else if (x <= 5.1e-138) {
		tmp = -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0066:
		tmp = y * x
	elif x <= 5.1e-138:
		tmp = -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0066)
		tmp = Float64(y * x);
	elseif (x <= 5.1e-138)
		tmp = Float64(-z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0066)
		tmp = y * x;
	elseif (x <= 5.1e-138)
		tmp = -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0066], N[(y * x), $MachinePrecision], If[LessEqual[x, 5.1e-138], (-z), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 5.1000000000000002e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 54.4%

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

   if -0.0066 < x < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. sub-neg 97.2%

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

   3. distribute-rgt-in 97.2%

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

   4. metadata-eval 97.2%

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

   5. neg-mul-1 97.2%

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

   6. unsub-neg 97.2%

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

   7. associate-+r- 97.2%

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

   8. distribute-lft-out 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 8: 37.6% 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 97.2%

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

2. Taylor expanded in x around 0 32.4%

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

   1. mul-1-neg 32.4%

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

4. Simplified 32.4%

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

5. Final simplification 32.4%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))