(cos (* (atan (* (tan (- (* z0 (+ PI PI)) (* -1/2 PI))) (/ z1 z2))) -2))

Percentage Accurate: 82.3% → 99.9%

Time: 16.0s

Alternatives: 2

Speedup: 1.0×

• could not determine a ground truth

  1. z0 = 6.933255579494087e+50
  2. z1 = 1.4239788943817417e+126
  3. z2 = 6.179446916570151e-97

Specification

Math

\[\cos \left(\tan^{-1} \left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right) \cdot -2\right) \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (cos
 (* (atan (* (tan (- (* z0 (+ PI PI)) (* -1/2 PI))) (/ z1 z2))) -2)))

C

double code(double z0, double z1, double z2) {
	return cos((atan((tan(((z0 * (((double) M_PI) + ((double) M_PI))) - (-0.5 * ((double) M_PI)))) * (z1 / z2))) * -2.0));
}

Java

public static double code(double z0, double z1, double z2) {
	return Math.cos((Math.atan((Math.tan(((z0 * (Math.PI + Math.PI)) - (-0.5 * Math.PI))) * (z1 / z2))) * -2.0));
}

Python

def code(z0, z1, z2):
	return math.cos((math.atan((math.tan(((z0 * (math.pi + math.pi)) - (-0.5 * math.pi))) * (z1 / z2))) * -2.0))

Julia

function code(z0, z1, z2)
	return cos(Float64(atan(Float64(tan(Float64(Float64(z0 * Float64(pi + pi)) - Float64(-0.5 * pi))) * Float64(z1 / z2))) * -2.0))
end

MATLAB

function tmp = code(z0, z1, z2)
	tmp = cos((atan((tan(((z0 * (pi + pi)) - (-0.5 * pi))) * (z1 / z2))) * -2.0));
end

Wolfram

code[z0_, z1_, z2_] := N[Cos[N[(N[ArcTan[N[(N[Tan[N[(N[(z0 * N[(Pi + Pi), $MachinePrecision]), $MachinePrecision] - N[(-1/2 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(z1 / z2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * -2), $MachinePrecision]], $MachinePrecision]

Initial Program: 82.3% accurate, 1.0× speedup

Math

\[\cos \left(\tan^{-1} \left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right) \cdot -2\right) \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (cos
 (* (atan (* (tan (- (* z0 (+ PI PI)) (* -1/2 PI))) (/ z1 z2))) -2)))

C

double code(double z0, double z1, double z2) {
	return cos((atan((tan(((z0 * (((double) M_PI) + ((double) M_PI))) - (-0.5 * ((double) M_PI)))) * (z1 / z2))) * -2.0));
}

Java

public static double code(double z0, double z1, double z2) {
	return Math.cos((Math.atan((Math.tan(((z0 * (Math.PI + Math.PI)) - (-0.5 * Math.PI))) * (z1 / z2))) * -2.0));
}

Python

def code(z0, z1, z2):
	return math.cos((math.atan((math.tan(((z0 * (math.pi + math.pi)) - (-0.5 * math.pi))) * (z1 / z2))) * -2.0))

Julia

function code(z0, z1, z2)
	return cos(Float64(atan(Float64(tan(Float64(Float64(z0 * Float64(pi + pi)) - Float64(-0.5 * pi))) * Float64(z1 / z2))) * -2.0))
end

MATLAB

function tmp = code(z0, z1, z2)
	tmp = cos((atan((tan(((z0 * (pi + pi)) - (-0.5 * pi))) * (z1 / z2))) * -2.0));
end

Wolfram

code[z0_, z1_, z2_] := N[Cos[N[(N[ArcTan[N[(N[Tan[N[(N[(z0 * N[(Pi + Pi), $MachinePrecision]), $MachinePrecision] - N[(-1/2 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(z1 / z2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * -2), $MachinePrecision]], $MachinePrecision]

Alternative 1: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := \left(\pi + \pi\right) \cdot z0\\ \cos \left(\tan^{-1} \left(\frac{\cos t\_0 \cdot z1}{\left(-\sin t\_0\right) \cdot z2}\right) \cdot -2\right) \end{array} \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (let* ((t_0 (* (+ PI PI) z0)))
  (cos (* (atan (/ (* (cos t_0) z1) (* (- (sin t_0)) z2))) -2))))

C

double code(double z0, double z1, double z2) {
	double t_0 = (((double) M_PI) + ((double) M_PI)) * z0;
	return cos((atan(((cos(t_0) * z1) / (-sin(t_0) * z2))) * -2.0));
}

Java

public static double code(double z0, double z1, double z2) {
	double t_0 = (Math.PI + Math.PI) * z0;
	return Math.cos((Math.atan(((Math.cos(t_0) * z1) / (-Math.sin(t_0) * z2))) * -2.0));
}

Python

def code(z0, z1, z2):
	t_0 = (math.pi + math.pi) * z0
	return math.cos((math.atan(((math.cos(t_0) * z1) / (-math.sin(t_0) * z2))) * -2.0))

Julia

function code(z0, z1, z2)
	t_0 = Float64(Float64(pi + pi) * z0)
	return cos(Float64(atan(Float64(Float64(cos(t_0) * z1) / Float64(Float64(-sin(t_0)) * z2))) * -2.0))
end

MATLAB

function tmp = code(z0, z1, z2)
	t_0 = (pi + pi) * z0;
	tmp = cos((atan(((cos(t_0) * z1) / (-sin(t_0) * z2))) * -2.0));
end

Wolfram

code[z0_, z1_, z2_] := Block[{t$95$0 = N[(N[(Pi + Pi), $MachinePrecision] * z0), $MachinePrecision]}, N[Cos[N[(N[ArcTan[N[(N[(N[Cos[t$95$0], $MachinePrecision] * z1), $MachinePrecision] / N[((-N[Sin[t$95$0], $MachinePrecision]) * z2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * -2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Initial program 82.3%

   \[\cos \left(\tan^{-1} \left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right) \cdot -2\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right)} \cdot -2\right) \]

   2. lift-tan.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \left(\color{blue}{\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right)} \cdot \frac{z1}{z2}\right) \cdot -2\right) \]

   3. tan-quot N/A

      \[\leadsto \cos \left(\tan^{-1} \left(\color{blue}{\frac{\sin \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right)}{\cos \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right)}} \cdot \frac{z1}{z2}\right) \cdot -2\right) \]

   4. lift-/.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \left(\frac{\sin \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right)}{\cos \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right)} \cdot \color{blue}{\frac{z1}{z2}}\right) \cdot -2\right) \]

   5. frac-times N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{\sin \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z1}{\cos \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z2}\right)} \cdot -2\right) \]

   6. lower-/.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{\sin \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z1}{\cos \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z2}\right)} \cdot -2\right) \]

3. Applied rewrites 99.9%

   \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{\cos \left(\left(\pi + \pi\right) \cdot z0\right) \cdot z1}{\left(-\sin \left(\left(\pi + \pi\right) \cdot z0\right)\right) \cdot z2}\right)} \cdot -2\right) \]
4. Add Preprocessing

Alternative 2: 82.3% accurate, 1.0× speedup

Math

\[\cos \left(\tan^{-1} \left(\frac{z1 \cdot \tan \left(\pi \cdot \left(\frac{1}{2} + \left(z0 + z0\right)\right)\right)}{z2}\right) \cdot -2\right) \]

FPCore

(FPCore (z0 z1 z2)
  :precision binary64
  (cos (* (atan (/ (* z1 (tan (* PI (+ 1/2 (+ z0 z0))))) z2)) -2)))

C

double code(double z0, double z1, double z2) {
	return cos((atan(((z1 * tan((((double) M_PI) * (0.5 + (z0 + z0))))) / z2)) * -2.0));
}

Java

public static double code(double z0, double z1, double z2) {
	return Math.cos((Math.atan(((z1 * Math.tan((Math.PI * (0.5 + (z0 + z0))))) / z2)) * -2.0));
}

Python

def code(z0, z1, z2):
	return math.cos((math.atan(((z1 * math.tan((math.pi * (0.5 + (z0 + z0))))) / z2)) * -2.0))

Julia

function code(z0, z1, z2)
	return cos(Float64(atan(Float64(Float64(z1 * tan(Float64(pi * Float64(0.5 + Float64(z0 + z0))))) / z2)) * -2.0))
end

MATLAB

function tmp = code(z0, z1, z2)
	tmp = cos((atan(((z1 * tan((pi * (0.5 + (z0 + z0))))) / z2)) * -2.0));
end

Wolfram

code[z0_, z1_, z2_] := N[Cos[N[(N[ArcTan[N[(N[(z1 * N[Tan[N[(Pi * N[(1/2 + N[(z0 + z0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]], $MachinePrecision] * -2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 82.3%

   \[\cos \left(\tan^{-1} \left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right) \cdot -2\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \frac{z1}{z2}\right)} \cdot -2\right) \]

   2. lift-/.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \left(\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot \color{blue}{\frac{z1}{z2}}\right) \cdot -2\right) \]

   3. associate-*r/ N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z1}{z2}\right)} \cdot -2\right) \]

   4. lower-/.f64 N/A

      \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{\tan \left(z0 \cdot \left(\pi + \pi\right) - \frac{-1}{2} \cdot \pi\right) \cdot z1}{z2}\right)} \cdot -2\right) \]

3. Applied rewrites 82.3%

   \[\leadsto \cos \left(\tan^{-1} \color{blue}{\left(\frac{z1 \cdot \tan \left(\pi \cdot \left(\frac{1}{2} + \left(z0 + z0\right)\right)\right)}{z2}\right)} \cdot -2\right) \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2025277 -o generate:taylor -o generate:evaluate
(FPCore (z0 z1 z2)
  :name "(cos (* (atan (* (tan (- (* z0 (+ PI PI)) (* -1/2 PI))) (/ z1 z2))) -2))"
  :precision binary64
  (cos (* (atan (* (tan (- (* z0 (+ PI PI)) (* -1/2 PI))) (/ z1 z2))) -2)))