(sin (* z1 (* PI z0)))

Percentage Accurate: 52.2% → 96.3%

Time: 3.8s

Alternatives: 6

Speedup: 0.3×

Specification

Math

\[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (sin (* z1 (* PI z0))))

C

double code(double z1, double z0) {
	return sin((z1 * (((double) M_PI) * z0)));
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 52.2% accurate, 1.0× speedup

Math

\[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (sin (* z1 (* PI z0))))

C

double code(double z1, double z0) {
	return sin((z1 * (((double) M_PI) * z0)));
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.3× speedup

Math

\[\mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \begin{array}{l} \mathbf{if}\;\left|z1\right| \cdot \left(\pi \cdot \left|z0\right|\right) \leq 4 \cdot 10^{+31}:\\ \;\;\;\;\sin \left(\left(\left|z0\right| \cdot \left|z1\right|\right) \cdot \pi\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(\left|z1\right| \cdot \log 1\right)\\ \end{array}\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (*
 (copysign 1.0 z1)
 (*
  (copysign 1.0 z0)
  (if (<= (* (fabs z1) (* PI (fabs z0))) 4e+31)
    (sin (* (* (fabs z0) (fabs z1)) PI))
    (sin (* (fabs z1) (log 1.0)))))))

C

double code(double z1, double z0) {
	double tmp;
	if ((fabs(z1) * (((double) M_PI) * fabs(z0))) <= 4e+31) {
		tmp = sin(((fabs(z0) * fabs(z1)) * ((double) M_PI)));
	} else {
		tmp = sin((fabs(z1) * log(1.0)));
	}
	return copysign(1.0, z1) * (copysign(1.0, z0) * tmp);
}

Java

public static double code(double z1, double z0) {
	double tmp;
	if ((Math.abs(z1) * (Math.PI * Math.abs(z0))) <= 4e+31) {
		tmp = Math.sin(((Math.abs(z0) * Math.abs(z1)) * Math.PI));
	} else {
		tmp = Math.sin((Math.abs(z1) * Math.log(1.0)));
	}
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * tmp);
}

Python

def code(z1, z0):
	tmp = 0
	if (math.fabs(z1) * (math.pi * math.fabs(z0))) <= 4e+31:
		tmp = math.sin(((math.fabs(z0) * math.fabs(z1)) * math.pi))
	else:
		tmp = math.sin((math.fabs(z1) * math.log(1.0)))
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * tmp)

Julia

function code(z1, z0)
	tmp = 0.0
	if (Float64(abs(z1) * Float64(pi * abs(z0))) <= 4e+31)
		tmp = sin(Float64(Float64(abs(z0) * abs(z1)) * pi));
	else
		tmp = sin(Float64(abs(z1) * log(1.0)));
	end
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * tmp))
end

MATLAB

function tmp_2 = code(z1, z0)
	tmp = 0.0;
	if ((abs(z1) * (pi * abs(z0))) <= 4e+31)
		tmp = sin(((abs(z0) * abs(z1)) * pi));
	else
		tmp = sin((abs(z1) * log(1.0)));
	end
	tmp_2 = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * tmp);
end

Wolfram

code[z1_, z0_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[Abs[z1], $MachinePrecision] * N[(Pi * N[Abs[z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e+31], N[Sin[N[(N[(N[Abs[z0], $MachinePrecision] * N[Abs[z1], $MachinePrecision]), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision], N[Sin[N[(N[Abs[z1], $MachinePrecision] * N[Log[1.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z1 (*.f64 (PI.f64) z0)) < 3.9999999999999999e31

   1. Initial program 52.2%

      \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 52.1%

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

   3. Applied rewrites 52.1%

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

   if 3.9999999999999999e31 < (*.f64 z1 (*.f64 (PI.f64) z0))

   1. Initial program 52.2%

      \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-PI.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right)\right) \]

      4. add-cube-cbrt N/A

         \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{PI}\left(\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\left(z0 \cdot \left(\sqrt[3]{\mathsf{PI}\left(\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\left(z0 \cdot \left(\sqrt[3]{\mathsf{PI}\left(\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \sin \left(z1 \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\mathsf{PI}\left(\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right) \cdot z0\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\mathsf{PI}\left(\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right) \cdot z0\right)} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      9. lift-PI.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(\left(\left(\sqrt[3]{\color{blue}{\pi}} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right) \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      10. pow1/3 N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left(\left(\color{blue}{{\pi}^{\frac{1}{3}}} \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right) \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      11. lift-PI.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left(\left({\pi}^{\frac{1}{3}} \cdot \sqrt[3]{\color{blue}{\pi}}\right) \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      12. pow1/3 N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left(\left({\pi}^{\frac{1}{3}} \cdot \color{blue}{{\pi}^{\frac{1}{3}}}\right) \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      13. pow-prod-up N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left(\color{blue}{{\pi}^{\left(\frac{1}{3} + \frac{1}{3}\right)}} \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      14. lower-pow.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left(\color{blue}{{\pi}^{\left(\frac{1}{3} + \frac{1}{3}\right)}} \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left({\pi}^{\color{blue}{\frac{2}{3}}} \cdot z0\right) \cdot \sqrt[3]{\mathsf{PI}\left(\right)}\right)\right) \]

      16. lift-PI.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \left(\left({\pi}^{\frac{2}{3}} \cdot z0\right) \cdot \sqrt[3]{\color{blue}{\pi}}\right)\right) \]

      17. lower-cbrt.f64 51.8%

          \[\leadsto \sin \left(z1 \cdot \left(\left({\pi}^{0.6666666666666666} \cdot z0\right) \cdot \color{blue}{\sqrt[3]{\pi}}\right)\right) \]

   3. Applied rewrites 51.8%

      \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\left({\pi}^{0.6666666666666666} \cdot z0\right) \cdot \sqrt[3]{\pi}\right)}\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\left({\pi}^{\frac{2}{3}} \cdot z0\right) \cdot \sqrt[3]{\pi}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\sqrt[3]{\pi} \cdot \left({\pi}^{\frac{2}{3}} \cdot z0\right)\right)}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(\sqrt[3]{\pi} \cdot \color{blue}{\left({\pi}^{\frac{2}{3}} \cdot z0\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \sin \left(z1 \cdot \left(\sqrt[3]{\pi} \cdot \color{blue}{\left(z0 \cdot {\pi}^{\frac{2}{3}}\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(\left(\sqrt[3]{\pi} \cdot z0\right) \cdot {\pi}^{\frac{2}{3}}\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \sin \left(z1 \cdot \left(\color{blue}{\left(z0 \cdot \sqrt[3]{\pi}\right)} \cdot {\pi}^{\frac{2}{3}}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \sin \left(z1 \cdot \color{blue}{\left(z0 \cdot \left(\sqrt[3]{\pi} \cdot {\pi}^{\frac{2}{3}}\right)\right)}\right) \]

      8. lift-cbrt.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\color{blue}{\sqrt[3]{\pi}} \cdot {\pi}^{\frac{2}{3}}\right)\right)\right) \]

      9. lift-pow.f64 N/A

         \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\sqrt[3]{\pi} \cdot \color{blue}{{\pi}^{\frac{2}{3}}}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\sqrt[3]{\pi} \cdot {\pi}^{\color{blue}{\left(2 \cdot \frac{1}{3}\right)}}\right)\right)\right) \]

      11. pow-sqr N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\sqrt[3]{\pi} \cdot \color{blue}{\left({\pi}^{\frac{1}{3}} \cdot {\pi}^{\frac{1}{3}}\right)}\right)\right)\right) \]

      12. pow1/3 N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\sqrt[3]{\pi} \cdot \left(\color{blue}{\sqrt[3]{\pi}} \cdot {\pi}^{\frac{1}{3}}\right)\right)\right)\right) \]

      13. pow1/3 N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \left(\sqrt[3]{\pi} \cdot \left(\sqrt[3]{\pi} \cdot \color{blue}{\sqrt[3]{\pi}}\right)\right)\right)\right) \]

      14. rem-3cbrt-rft N/A

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

      15. rem-log-exp N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \color{blue}{\log \left(e^{\pi}\right)}\right)\right) \]

      16. lift-PI.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \left(z0 \cdot \log \left(e^{\color{blue}{\mathsf{PI}\left(\right)}}\right)\right)\right) \]

      17. log-pow-rev N/A

          \[\leadsto \sin \left(z1 \cdot \color{blue}{\log \left({\left(e^{\mathsf{PI}\left(\right)}\right)}^{z0}\right)}\right) \]

      18. lower-log.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \color{blue}{\log \left({\left(e^{\mathsf{PI}\left(\right)}\right)}^{z0}\right)}\right) \]

      19. lift-PI.f64 N/A

          \[\leadsto \sin \left(z1 \cdot \log \left({\left(e^{\color{blue}{\pi}}\right)}^{z0}\right)\right) \]

      20. pow-exp N/A

          \[\leadsto \sin \left(z1 \cdot \log \color{blue}{\left(e^{\pi \cdot z0}\right)}\right) \]

      21. *-commutative N/A

          \[\leadsto \sin \left(z1 \cdot \log \left(e^{\color{blue}{z0 \cdot \pi}}\right)\right) \]

   5. Applied rewrites 23.7%

      \[\leadsto \sin \left(z1 \cdot \color{blue}{\log \left(e^{\pi \cdot z0}\right)}\right) \]

   6. Taylor expanded in z0 around 0

      \[\leadsto \sin \left(z1 \cdot \log \color{blue}{1}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 59.1%

      \[\leadsto \sin \left(z1 \cdot \log \color{blue}{1}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 52.2% accurate, 1.0× speedup

Math

\[\sin \left(\left(z0 \cdot z1\right) \cdot \pi\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (sin (* (* z0 z1) PI)))

C

double code(double z1, double z0) {
	return sin(((z0 * z1) * ((double) M_PI)));
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.2%

   \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 52.1%

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

3. Applied rewrites 52.1%

   \[\leadsto \sin \color{blue}{\left(\left(z0 \cdot z1\right) \cdot \pi\right)} \]
4. Add Preprocessing

Alternative 3: 52.1% accurate, 0.2× speedup

Math

\[\mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \sin \left(\mathsf{min}\left(\left|z1\right|, \left|z0\right|\right) \cdot \left(\pi \cdot \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\right)\right)\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (*
 (copysign 1.0 z1)
 (*
  (copysign 1.0 z0)
  (sin
   (* (fmin (fabs z1) (fabs z0)) (* PI (fmax (fabs z1) (fabs z0))))))))

C

double code(double z1, double z0) {
	return copysign(1.0, z1) * (copysign(1.0, z0) * sin((fmin(fabs(z1), fabs(z0)) * (((double) M_PI) * fmax(fabs(z1), fabs(z0))))));
}

Java

public static double code(double z1, double z0) {
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * Math.sin((fmin(Math.abs(z1), Math.abs(z0)) * (Math.PI * fmax(Math.abs(z1), Math.abs(z0))))));
}

Python

def code(z1, z0):
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * math.sin((fmin(math.fabs(z1), math.fabs(z0)) * (math.pi * fmax(math.fabs(z1), math.fabs(z0))))))

Julia

function code(z1, z0)
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * sin(Float64(fmin(abs(z1), abs(z0)) * Float64(pi * fmax(abs(z1), abs(z0)))))))
end

MATLAB

function tmp = code(z1, z0)
	tmp = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * sin((min(abs(z1), abs(z0)) * (pi * max(abs(z1), abs(z0))))));
end

Wolfram

code[z1_, z0_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[Sin[N[(N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision] * N[(Pi * N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.2%

   \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]
2. Add Preprocessing

Alternative 4: 50.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|z1\right|, \left|z0\right|\right)\\ t_1 := \mathsf{max}\left(\left|z1\right|, \left|z0\right|\right)\\ t_2 := t\_1 \cdot t\_0\\ \mathsf{copysign}\left(1, z1\right) \cdot \left(\mathsf{copysign}\left(1, z0\right) \cdot \left(\left(\left(\left(\left(\left(-0.16666666666666666 \cdot t\_0\right) \cdot \pi\right) \cdot \pi\right) \cdot t\_2\right) \cdot t\_1 + 1\right) \cdot \left(t\_2 \cdot \pi\right)\right)\right) \end{array} \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (let* ((t_0 (fmin (fabs z1) (fabs z0)))
       (t_1 (fmax (fabs z1) (fabs z0)))
       (t_2 (* t_1 t_0)))
  (*
   (copysign 1.0 z1)
   (*
    (copysign 1.0 z0)
    (*
     (+
      (* (* (* (* (* -0.16666666666666666 t_0) PI) PI) t_2) t_1)
      1.0)
     (* t_2 PI))))))

C

double code(double z1, double z0) {
	double t_0 = fmin(fabs(z1), fabs(z0));
	double t_1 = fmax(fabs(z1), fabs(z0));
	double t_2 = t_1 * t_0;
	return copysign(1.0, z1) * (copysign(1.0, z0) * (((((((-0.16666666666666666 * t_0) * ((double) M_PI)) * ((double) M_PI)) * t_2) * t_1) + 1.0) * (t_2 * ((double) M_PI))));
}

Java

public static double code(double z1, double z0) {
	double t_0 = fmin(Math.abs(z1), Math.abs(z0));
	double t_1 = fmax(Math.abs(z1), Math.abs(z0));
	double t_2 = t_1 * t_0;
	return Math.copySign(1.0, z1) * (Math.copySign(1.0, z0) * (((((((-0.16666666666666666 * t_0) * Math.PI) * Math.PI) * t_2) * t_1) + 1.0) * (t_2 * Math.PI)));
}

Python

def code(z1, z0):
	t_0 = fmin(math.fabs(z1), math.fabs(z0))
	t_1 = fmax(math.fabs(z1), math.fabs(z0))
	t_2 = t_1 * t_0
	return math.copysign(1.0, z1) * (math.copysign(1.0, z0) * (((((((-0.16666666666666666 * t_0) * math.pi) * math.pi) * t_2) * t_1) + 1.0) * (t_2 * math.pi)))

Julia

function code(z1, z0)
	t_0 = fmin(abs(z1), abs(z0))
	t_1 = fmax(abs(z1), abs(z0))
	t_2 = Float64(t_1 * t_0)
	return Float64(copysign(1.0, z1) * Float64(copysign(1.0, z0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(-0.16666666666666666 * t_0) * pi) * pi) * t_2) * t_1) + 1.0) * Float64(t_2 * pi))))
end

MATLAB

function tmp = code(z1, z0)
	t_0 = min(abs(z1), abs(z0));
	t_1 = max(abs(z1), abs(z0));
	t_2 = t_1 * t_0;
	tmp = (sign(z1) * abs(1.0)) * ((sign(z0) * abs(1.0)) * (((((((-0.16666666666666666 * t_0) * pi) * pi) * t_2) * t_1) + 1.0) * (t_2 * pi)));
end

Wolfram

code[z1_, z0_] := Block[{t$95$0 = N[Min[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[z1], $MachinePrecision], N[Abs[z0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$0), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z1]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(-0.16666666666666666 * t$95$0), $MachinePrecision] * Pi), $MachinePrecision] * Pi), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(t$95$2 * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 52.2%

   \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]

2. Taylor expanded in z1 around 0

   \[\leadsto \color{blue}{z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \color{blue}{\left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0 \cdot \mathsf{PI}\left(\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0} \cdot \mathsf{PI}\left(\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   5. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   8. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   9. lower-PI.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   11. lower-PI.f64 41.6%

       \[\leadsto z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right) \]

4. Applied rewrites 41.6%

   \[\leadsto \color{blue}{z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto z1 \cdot \color{blue}{\left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]

   2. lift-+.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + \color{blue}{z0 \cdot \pi}\right) \]

   3. distribute-lft-in N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) + \color{blue}{z1 \cdot \left(z0 \cdot \pi\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) + z1 \cdot \left(z0 \cdot \color{blue}{\pi}\right) \]

   5. associate-*l* N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) + \left(z1 \cdot z0\right) \cdot \color{blue}{\pi} \]

   6. *-commutative N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) + \left(z0 \cdot z1\right) \cdot \pi \]

   7. lift-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) + \left(z0 \cdot z1\right) \cdot \pi \]

   8. fp-cancel-sign-sub-inv N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z0 \cdot z1\right)\right) \cdot \pi} \]

   9. lower--.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right)\right) - \color{blue}{\left(\mathsf{neg}\left(z0 \cdot z1\right)\right) \cdot \pi} \]

6. Applied rewrites 41.4%

   \[\leadsto \left(-0.16666666666666666 \cdot z1\right) \cdot \left(\left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z0\right) \cdot z0\right)\right) - \color{blue}{\left(\left(-z1\right) \cdot z0\right) \cdot \pi} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z0\right) \cdot z0\right)\right) - \color{blue}{\left(\left(-z1\right) \cdot z0\right)} \cdot \pi \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z0\right) \cdot z0\right)\right) - \left(\left(-z1\right) \cdot \color{blue}{z0}\right) \cdot \pi \]

   3. associate-*r* N/A

      \[\leadsto \left(\left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right)\right) \cdot \left(\left(z0 \cdot z0\right) \cdot z0\right) - \color{blue}{\left(\left(-z1\right) \cdot z0\right)} \cdot \pi \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right)\right) \cdot \left(\left(z0 \cdot z0\right) \cdot z0\right) - \left(\left(-z1\right) \cdot \color{blue}{z0}\right) \cdot \pi \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right)\right) \cdot \left(z0 \cdot z0\right)\right) \cdot z0 - \color{blue}{\left(\left(-z1\right) \cdot z0\right)} \cdot \pi \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \left(\left(\left(\left(z1 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \pi\right)\right) \cdot \left(z0 \cdot z0\right)\right) \cdot z0 - \color{blue}{\left(\left(-z1\right) \cdot z0\right)} \cdot \pi \]

8. Applied rewrites 49.9%

   \[\leadsto \left(\left(\left(-0.16666666666666666 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \color{blue}{\left(\left(-z1\right) \cdot z0\right)} \cdot \pi \]
9. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \color{blue}{\left(\left(-z1\right) \cdot z0\right) \cdot \pi} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\left(-z1\right) \cdot z0\right) \cdot \color{blue}{\pi} \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\left(-z1\right) \cdot z0\right) \cdot \pi \]

   4. lift-neg.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\left(\mathsf{neg}\left(z1\right)\right) \cdot z0\right) \cdot \pi \]

   5. distribute-lft-neg-out N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\mathsf{neg}\left(z1 \cdot z0\right)\right) \cdot \pi \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\mathsf{neg}\left(z0 \cdot z1\right)\right) \cdot \pi \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 - \left(\mathsf{neg}\left(z0 \cdot z1\right)\right) \cdot \pi \]

   8. fp-cancel-sign-sub N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 + \color{blue}{\left(z0 \cdot z1\right) \cdot \pi} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\frac{-1}{6} \cdot z1\right) \cdot \pi\right) \cdot \left(\left(\left(z0 \cdot z1\right) \cdot \pi\right) \cdot \left(\left(z0 \cdot z1\right) \cdot \pi\right)\right)\right) \cdot z0 + \left(z0 \cdot z1\right) \cdot \color{blue}{\pi} \]

10. Applied rewrites 50.1%

    \[\leadsto \left(\left(\left(\left(\left(-0.16666666666666666 \cdot z1\right) \cdot \pi\right) \cdot \pi\right) \cdot \left(z0 \cdot z1\right)\right) \cdot z0 + 1\right) \cdot \color{blue}{\left(\left(z0 \cdot z1\right) \cdot \pi\right)} \]
11. Add Preprocessing

Alternative 5: 50.1% accurate, 10.1× speedup

Math

\[\left(z0 \cdot z1\right) \cdot \pi \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (* (* z0 z1) PI))

C

double code(double z1, double z0) {
	return (z0 * z1) * ((double) M_PI);
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.2%

   \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]

2. Taylor expanded in z1 around 0

   \[\leadsto \color{blue}{z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \color{blue}{\left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0 \cdot \mathsf{PI}\left(\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0} \cdot \mathsf{PI}\left(\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   5. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   8. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   9. lower-PI.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   11. lower-PI.f64 41.6%

       \[\leadsto z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right) \]

4. Applied rewrites 41.6%

   \[\leadsto \color{blue}{z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]

5. Taylor expanded in z1 around 0

   \[\leadsto z1 \cdot \left(z0 \cdot \color{blue}{\pi}\right) \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) \]

   2. lower-PI.f64 50.1%

      \[\leadsto z1 \cdot \left(z0 \cdot \pi\right) \]

7. Applied rewrites 50.1%

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

8. Taylor expanded in z1 around 0

   \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot \pi\right)} \]
9. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z0 \cdot \left(z1 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto z0 \cdot \left(z1 \cdot \mathsf{PI}\left(\right)\right) \]

   3. lower-PI.f64 50.1%

      \[\leadsto z0 \cdot \left(z1 \cdot \pi\right) \]

10. Applied rewrites 50.1%

    \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot \pi\right)} \]
11. Step-by-step derivation

    1. lift-*.f64 N/A

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

    2. lift-*.f64 N/A

       \[\leadsto z0 \cdot \left(z1 \cdot \pi\right) \]

    3. associate-*l* N/A

       \[\leadsto \left(z0 \cdot z1\right) \cdot \pi \]

    4. lift-*.f64 N/A

       \[\leadsto \left(z0 \cdot z1\right) \cdot \pi \]

    5. lift-*.f64 50.1%

       \[\leadsto \left(z0 \cdot z1\right) \cdot \pi \]

12. Applied rewrites 50.1%

    \[\leadsto \left(z0 \cdot z1\right) \cdot \pi \]
13. Add Preprocessing

Alternative 6: 50.1% accurate, 10.1× speedup

Math

\[z0 \cdot \left(z1 \cdot \pi\right) \]

FPCore

(FPCore (z1 z0)
  :precision binary64
  (* z0 (* z1 PI)))

C

double code(double z1, double z0) {
	return z0 * (z1 * ((double) M_PI));
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 52.2%

   \[\sin \left(z1 \cdot \left(\pi \cdot z0\right)\right) \]

2. Taylor expanded in z1 around 0

   \[\leadsto \color{blue}{z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \color{blue}{\left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right)} \]

   2. lower-+.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0 \cdot \mathsf{PI}\left(\right)}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + \color{blue}{z0} \cdot \mathsf{PI}\left(\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   5. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   8. lower-pow.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\mathsf{PI}\left(\right)}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   9. lower-PI.f64 N/A

      \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \mathsf{PI}\left(\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto z1 \cdot \left(\frac{-1}{6} \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   11. lower-PI.f64 41.6%

       \[\leadsto z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right) \]

4. Applied rewrites 41.6%

   \[\leadsto \color{blue}{z1 \cdot \left(-0.16666666666666666 \cdot \left({z0}^{3} \cdot \left({z1}^{2} \cdot {\pi}^{3}\right)\right) + z0 \cdot \pi\right)} \]

5. Taylor expanded in z1 around 0

   \[\leadsto z1 \cdot \left(z0 \cdot \color{blue}{\pi}\right) \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z1 \cdot \left(z0 \cdot \mathsf{PI}\left(\right)\right) \]

   2. lower-PI.f64 50.1%

      \[\leadsto z1 \cdot \left(z0 \cdot \pi\right) \]

7. Applied rewrites 50.1%

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

8. Taylor expanded in z1 around 0

   \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot \pi\right)} \]
9. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z0 \cdot \left(z1 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto z0 \cdot \left(z1 \cdot \mathsf{PI}\left(\right)\right) \]

   3. lower-PI.f64 50.1%

      \[\leadsto z0 \cdot \left(z1 \cdot \pi\right) \]

10. Applied rewrites 50.1%

    \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot \pi\right)} \]
11. Add Preprocessing

Reproduce

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