(/ (* PI z0) z1)

Percentage Accurate: 99.6% → 99.6%
Time: 1.1s
Alternatives: 2
Speedup: N/A×

Specification

?
\[\frac{\pi \cdot z0}{z1} \]
(FPCore (z0 z1)
  :precision binary64
  (/ (* PI z0) z1))
double code(double z0, double z1) {
	return (((double) M_PI) * z0) / z1;
}

public static double code(double z0, double z1) {
	return (Math.PI * z0) / z1;
}

def code(z0, z1):
	return (math.pi * z0) / z1

function code(z0, z1)
	return Float64(Float64(pi * z0) / z1)
end

function tmp = code(z0, z1)
	tmp = (pi * z0) / z1;
end

code[z0_, z1_] := N[(N[(Pi * z0), $MachinePrecision] / z1), $MachinePrecision]

\frac{\pi \cdot z0}{z1}

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: 99.6% accurate, 1.0× speedup?

\[\frac{\pi \cdot z0}{z1} \]
(FPCore (z0 z1)
  :precision binary64
  (/ (* PI z0) z1))
double code(double z0, double z1) {
	return (((double) M_PI) * z0) / z1;
}

public static double code(double z0, double z1) {
	return (Math.PI * z0) / z1;
}

def code(z0, z1):
	return (math.pi * z0) / z1

function code(z0, z1)
	return Float64(Float64(pi * z0) / z1)
end

function tmp = code(z0, z1)
	tmp = (pi * z0) / z1;
end

code[z0_, z1_] := N[(N[(Pi * z0), $MachinePrecision] / z1), $MachinePrecision]

\frac{\pi \cdot z0}{z1}

Alternative 1: 99.6% accurate, 1.0× speedup?

\[\frac{\pi}{z1} \cdot z0 \]
(FPCore (z0 z1)
  :precision binary64
  (* (/ PI z1) z0))
double code(double z0, double z1) {
	return (((double) M_PI) / z1) * z0;
}

public static double code(double z0, double z1) {
	return (Math.PI / z1) * z0;
}

def code(z0, z1):
	return (math.pi / z1) * z0

function code(z0, z1)
	return Float64(Float64(pi / z1) * z0)
end

function tmp = code(z0, z1)
	tmp = (pi / z1) * z0;
end

code[z0_, z1_] := N[(N[(Pi / z1), $MachinePrecision] * z0), $MachinePrecision]

\frac{\pi}{z1} \cdot z0
Derivation

  1. Initial program 99.6%

    \[\frac{\pi \cdot z0}{z1} \]
  2. Step-by-step derivation

    1. lift-/.f64N/A

      \[\leadsto \color{blue}{\frac{\pi \cdot z0}{z1}} \]

    2. mult-flipN/A

      \[\leadsto \color{blue}{\left(\pi \cdot z0\right) \cdot \frac{1}{z1}} \]

    3. lift-*.f64N/A

      \[\leadsto \color{blue}{\left(\pi \cdot z0\right)} \cdot \frac{1}{z1} \]

    4. *-commutativeN/A

      \[\leadsto \color{blue}{\left(z0 \cdot \pi\right)} \cdot \frac{1}{z1} \]

    5. associate-*l*N/A

      \[\leadsto \color{blue}{z0 \cdot \left(\pi \cdot \frac{1}{z1}\right)} \]

    6. *-commutativeN/A

      \[\leadsto \color{blue}{\left(\pi \cdot \frac{1}{z1}\right) \cdot z0} \]

    7. lower-*.f64N/A

      \[\leadsto \color{blue}{\left(\pi \cdot \frac{1}{z1}\right) \cdot z0} \]

    8. mult-flip-revN/A

      \[\leadsto \color{blue}{\frac{\pi}{z1}} \cdot z0 \]

    9. lower-/.f6499.6%

      \[\leadsto \color{blue}{\frac{\pi}{z1}} \cdot z0 \]

  3. Applied rewrites99.6%

    \[\leadsto \color{blue}{\frac{\pi}{z1} \cdot z0} \]
  4. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup?

\[\frac{z0}{z1} \cdot \pi \]
(FPCore (z0 z1)
  :precision binary64
  (* (/ z0 z1) PI))
double code(double z0, double z1) {
	return (z0 / z1) * ((double) M_PI);
}

public static double code(double z0, double z1) {
	return (z0 / z1) * Math.PI;
}

def code(z0, z1):
	return (z0 / z1) * math.pi

function code(z0, z1)
	return Float64(Float64(z0 / z1) * pi)
end

function tmp = code(z0, z1)
	tmp = (z0 / z1) * pi;
end

code[z0_, z1_] := N[(N[(z0 / z1), $MachinePrecision] * Pi), $MachinePrecision]

\frac{z0}{z1} \cdot \pi
Derivation

  1. Initial program 99.6%

    \[\frac{\pi \cdot z0}{z1} \]
  2. Step-by-step derivation

    1. lift-/.f64N/A

      \[\leadsto \color{blue}{\frac{\pi \cdot z0}{z1}} \]

    2. lift-*.f64N/A

      \[\leadsto \frac{\color{blue}{\pi \cdot z0}}{z1} \]

    3. associate-/l*N/A

      \[\leadsto \color{blue}{\pi \cdot \frac{z0}{z1}} \]

    4. *-commutativeN/A

      \[\leadsto \color{blue}{\frac{z0}{z1} \cdot \pi} \]

    5. lower-*.f64N/A

      \[\leadsto \color{blue}{\frac{z0}{z1} \cdot \pi} \]

    6. lower-/.f6499.6%

      \[\leadsto \color{blue}{\frac{z0}{z1}} \cdot \pi \]

  3. Applied rewrites99.6%

    \[\leadsto \color{blue}{\frac{z0}{z1} \cdot \pi} \]
  4. Add Preprocessing

Reproduce

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herbie shell --seed 2025250 
(FPCore (z0 z1)
  :name "(/ (* PI z0) z1)"
  :precision binary64
  (/ (* PI z0) z1))