(sin (* (* PI z0) 1/180))

Percentage Accurate: 56.6% → 56.7%
Time: 2.7s
Alternatives: 2
Speedup: 1.0×

Specification

?
\[\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right) \]
(FPCore (z0)
  :precision binary64
  (sin (* (* PI z0) 1/180)))
double code(double z0) {
	return sin(((((double) M_PI) * z0) * 0.005555555555555556));
}

public static double code(double z0) {
	return Math.sin(((Math.PI * z0) * 0.005555555555555556));
}

def code(z0):
	return math.sin(((math.pi * z0) * 0.005555555555555556))

function code(z0)
	return sin(Float64(Float64(pi * z0) * 0.005555555555555556))
end

function tmp = code(z0)
	tmp = sin(((pi * z0) * 0.005555555555555556));
end

code[z0_] := N[Sin[N[(N[(Pi * z0), $MachinePrecision] * 1/180), $MachinePrecision]], $MachinePrecision]

\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right)

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 2 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 56.6% accurate, 1.0× speedup?

\[\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right) \]
(FPCore (z0)
  :precision binary64
  (sin (* (* PI z0) 1/180)))
double code(double z0) {
	return sin(((((double) M_PI) * z0) * 0.005555555555555556));
}

public static double code(double z0) {
	return Math.sin(((Math.PI * z0) * 0.005555555555555556));
}

def code(z0):
	return math.sin(((math.pi * z0) * 0.005555555555555556))

function code(z0)
	return sin(Float64(Float64(pi * z0) * 0.005555555555555556))
end

function tmp = code(z0)
	tmp = sin(((pi * z0) * 0.005555555555555556));
end

code[z0_] := N[Sin[N[(N[(Pi * z0), $MachinePrecision] * 1/180), $MachinePrecision]], $MachinePrecision]

\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right)

Alternative 1: 56.7% accurate, 1.0× speedup?

\[\sin \left(\left(\frac{1}{180} \cdot \pi\right) \cdot z0\right) \]
(FPCore (z0)
  :precision binary64
  (sin (* (* 1/180 PI) z0)))
double code(double z0) {
	return sin(((0.005555555555555556 * ((double) M_PI)) * z0));
}

public static double code(double z0) {
	return Math.sin(((0.005555555555555556 * Math.PI) * z0));
}

def code(z0):
	return math.sin(((0.005555555555555556 * math.pi) * z0))

function code(z0)
	return sin(Float64(Float64(0.005555555555555556 * pi) * z0))
end

function tmp = code(z0)
	tmp = sin(((0.005555555555555556 * pi) * z0));
end

code[z0_] := N[Sin[N[(N[(1/180 * Pi), $MachinePrecision] * z0), $MachinePrecision]], $MachinePrecision]

\sin \left(\left(\frac{1}{180} \cdot \pi\right) \cdot z0\right)
Derivation

  1. Initial program 56.6%

    \[\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right) \]
  2. Step-by-step derivation

    1. lift-*.f64N/A

      \[\leadsto \sin \color{blue}{\left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right)} \]

    2. *-commutativeN/A

      \[\leadsto \sin \color{blue}{\left(\frac{1}{180} \cdot \left(\pi \cdot z0\right)\right)} \]

    3. lift-*.f64N/A

      \[\leadsto \sin \left(\frac{1}{180} \cdot \color{blue}{\left(\pi \cdot z0\right)}\right) \]

    4. associate-*r*N/A

      \[\leadsto \sin \color{blue}{\left(\left(\frac{1}{180} \cdot \pi\right) \cdot z0\right)} \]

    5. lower-*.f64N/A

      \[\leadsto \sin \color{blue}{\left(\left(\frac{1}{180} \cdot \pi\right) \cdot z0\right)} \]

    6. lower-*.f6456.7%

      \[\leadsto \sin \left(\color{blue}{\left(\frac{1}{180} \cdot \pi\right)} \cdot z0\right) \]

  3. Applied rewrites56.7%

    \[\leadsto \sin \color{blue}{\left(\left(\frac{1}{180} \cdot \pi\right) \cdot z0\right)} \]
  4. Add Preprocessing

Alternative 2: 56.7% accurate, 1.0× speedup?

\[\sin \left(\left(\frac{1}{180} \cdot z0\right) \cdot \pi\right) \]
(FPCore (z0)
  :precision binary64
  (sin (* (* 1/180 z0) PI)))
double code(double z0) {
	return sin(((0.005555555555555556 * z0) * ((double) M_PI)));
}

public static double code(double z0) {
	return Math.sin(((0.005555555555555556 * z0) * Math.PI));
}

def code(z0):
	return math.sin(((0.005555555555555556 * z0) * math.pi))

function code(z0)
	return sin(Float64(Float64(0.005555555555555556 * z0) * pi))
end

function tmp = code(z0)
	tmp = sin(((0.005555555555555556 * z0) * pi));
end

code[z0_] := N[Sin[N[(N[(1/180 * z0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]

\sin \left(\left(\frac{1}{180} \cdot z0\right) \cdot \pi\right)
Derivation

  1. Initial program 56.6%

    \[\sin \left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right) \]
  2. Step-by-step derivation

    1. lift-*.f64N/A

      \[\leadsto \sin \color{blue}{\left(\left(\pi \cdot z0\right) \cdot \frac{1}{180}\right)} \]

    2. lift-*.f64N/A

      \[\leadsto \sin \left(\color{blue}{\left(\pi \cdot z0\right)} \cdot \frac{1}{180}\right) \]

    3. associate-*l*N/A

      \[\leadsto \sin \color{blue}{\left(\pi \cdot \left(z0 \cdot \frac{1}{180}\right)\right)} \]

    4. *-commutativeN/A

      \[\leadsto \sin \color{blue}{\left(\left(z0 \cdot \frac{1}{180}\right) \cdot \pi\right)} \]

    5. lower-*.f64N/A

      \[\leadsto \sin \color{blue}{\left(\left(z0 \cdot \frac{1}{180}\right) \cdot \pi\right)} \]

    6. *-commutativeN/A

      \[\leadsto \sin \left(\color{blue}{\left(\frac{1}{180} \cdot z0\right)} \cdot \pi\right) \]

    7. lower-*.f6456.7%

      \[\leadsto \sin \left(\color{blue}{\left(\frac{1}{180} \cdot z0\right)} \cdot \pi\right) \]

  3. Applied rewrites56.7%

    \[\leadsto \sin \color{blue}{\left(\left(\frac{1}{180} \cdot z0\right) \cdot \pi\right)} \]
  4. Add Preprocessing

Reproduce

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herbie shell --seed 2025277 -o generate:taylor -o generate:evaluate
(FPCore (z0)
  :name "(sin (* (* PI z0) 1/180))"
  :precision binary64
  (sin (* (* PI z0) 1/180)))