(+ (* (cos (* (+ PI PI) z4)) z3) (* (* z2 z1) z0))

Percentage Accurate: 73.1% → 98.0%

Time: 3.3s

Alternatives: 6

Speedup: 0.1×

Specification

Math

\[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (+ (* (cos (* (+ PI PI) z4)) z3) (* (* z2 z1) z0)))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	return (cos(((((double) M_PI) + ((double) M_PI)) * z4)) * z3) + ((z2 * z1) * z0);
}

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	return (Math.cos(((Math.PI + Math.PI) * z4)) * z3) + ((z2 * z1) * z0);
}

Python

def code(z4, z3, z2, z1, z0):
	return (math.cos(((math.pi + math.pi) * z4)) * z3) + ((z2 * z1) * z0)

Julia

function code(z4, z3, z2, z1, z0)
	return Float64(Float64(cos(Float64(Float64(pi + pi) * z4)) * z3) + Float64(Float64(z2 * z1) * z0))
end

MATLAB

function tmp = code(z4, z3, z2, z1, z0)
	tmp = (cos(((pi + pi) * z4)) * z3) + ((z2 * z1) * z0);
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := N[(N[(N[Cos[N[(N[(Pi + Pi), $MachinePrecision] * z4), $MachinePrecision]], $MachinePrecision] * z3), $MachinePrecision] + N[(N[(z2 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.1% accurate, 1.0× speedup

Math

\[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (+ (* (cos (* (+ PI PI) z4)) z3) (* (* z2 z1) z0)))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	return (cos(((((double) M_PI) + ((double) M_PI)) * z4)) * z3) + ((z2 * z1) * z0);
}

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	return (Math.cos(((Math.PI + Math.PI) * z4)) * z3) + ((z2 * z1) * z0);
}

Python

def code(z4, z3, z2, z1, z0):
	return (math.cos(((math.pi + math.pi) * z4)) * z3) + ((z2 * z1) * z0)

Julia

function code(z4, z3, z2, z1, z0)
	return Float64(Float64(cos(Float64(Float64(pi + pi) * z4)) * z3) + Float64(Float64(z2 * z1) * z0))
end

MATLAB

function tmp = code(z4, z3, z2, z1, z0)
	tmp = (cos(((pi + pi) * z4)) * z3) + ((z2 * z1) * z0);
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := N[(N[(N[Cos[N[(N[(Pi + Pi), $MachinePrecision] * z4), $MachinePrecision]], $MachinePrecision] * z3), $MachinePrecision] + N[(N[(z2 * z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_1 := \mathsf{max}\left(\mathsf{max}\left(z2, z1\right), t\_0\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(z2, z1\right), t\_0\right)\\ t_3 := \mathsf{min}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ \mathbf{if}\;t\_2 \leq 10^{-23}:\\ \;\;\;\;\left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\cos \left(\left(\left(z4 + z4\right) - 0.5\right) \cdot \pi + 0.5 \cdot \pi\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(t\_1 \cdot t\_2\right) \cdot t\_3\\ \mathbf{else}:\\ \;\;\;\;z3 + \left(t\_3 \cdot t\_2\right) \cdot t\_1\\ \end{array} \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (let* ((t_0 (fmax (fmin z2 z1) z0))
       (t_1 (fmax (fmax z2 z1) t_0))
       (t_2 (fmin (fmax z2 z1) t_0))
       (t_3 (fmin (fmin z2 z1) z0)))
  (if (<= t_2 1e-23)
    (+
     (*
      (+
       (* (sin (* PI z4)) (sin (+ (* PI z4) PI)))
       (* (- (cos (+ (* (- (+ z4 z4) 0.5) PI) (* 0.5 PI))) -1.0) 0.5))
      z3)
     (* (* t_1 t_2) t_3))
    (+ z3 (* (* t_3 t_2) t_1)))))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmax(fmin(z2, z1), z0);
	double t_1 = fmax(fmax(z2, z1), t_0);
	double t_2 = fmin(fmax(z2, z1), t_0);
	double t_3 = fmin(fmin(z2, z1), z0);
	double tmp;
	if (t_2 <= 1e-23) {
		tmp = (((sin((((double) M_PI) * z4)) * sin(((((double) M_PI) * z4) + ((double) M_PI)))) + ((cos(((((z4 + z4) - 0.5) * ((double) M_PI)) + (0.5 * ((double) M_PI)))) - -1.0) * 0.5)) * z3) + ((t_1 * t_2) * t_3);
	} else {
		tmp = z3 + ((t_3 * t_2) * t_1);
	}
	return tmp;
}

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmax(fmin(z2, z1), z0);
	double t_1 = fmax(fmax(z2, z1), t_0);
	double t_2 = fmin(fmax(z2, z1), t_0);
	double t_3 = fmin(fmin(z2, z1), z0);
	double tmp;
	if (t_2 <= 1e-23) {
		tmp = (((Math.sin((Math.PI * z4)) * Math.sin(((Math.PI * z4) + Math.PI))) + ((Math.cos(((((z4 + z4) - 0.5) * Math.PI) + (0.5 * Math.PI))) - -1.0) * 0.5)) * z3) + ((t_1 * t_2) * t_3);
	} else {
		tmp = z3 + ((t_3 * t_2) * t_1);
	}
	return tmp;
}

Python

def code(z4, z3, z2, z1, z0):
	t_0 = fmax(fmin(z2, z1), z0)
	t_1 = fmax(fmax(z2, z1), t_0)
	t_2 = fmin(fmax(z2, z1), t_0)
	t_3 = fmin(fmin(z2, z1), z0)
	tmp = 0
	if t_2 <= 1e-23:
		tmp = (((math.sin((math.pi * z4)) * math.sin(((math.pi * z4) + math.pi))) + ((math.cos(((((z4 + z4) - 0.5) * math.pi) + (0.5 * math.pi))) - -1.0) * 0.5)) * z3) + ((t_1 * t_2) * t_3)
	else:
		tmp = z3 + ((t_3 * t_2) * t_1)
	return tmp

Julia

function code(z4, z3, z2, z1, z0)
	t_0 = fmax(fmin(z2, z1), z0)
	t_1 = fmax(fmax(z2, z1), t_0)
	t_2 = fmin(fmax(z2, z1), t_0)
	t_3 = fmin(fmin(z2, z1), z0)
	tmp = 0.0
	if (t_2 <= 1e-23)
		tmp = Float64(Float64(Float64(Float64(sin(Float64(pi * z4)) * sin(Float64(Float64(pi * z4) + pi))) + Float64(Float64(cos(Float64(Float64(Float64(Float64(z4 + z4) - 0.5) * pi) + Float64(0.5 * pi))) - -1.0) * 0.5)) * z3) + Float64(Float64(t_1 * t_2) * t_3));
	else
		tmp = Float64(z3 + Float64(Float64(t_3 * t_2) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z4, z3, z2, z1, z0)
	t_0 = max(min(z2, z1), z0);
	t_1 = max(max(z2, z1), t_0);
	t_2 = min(max(z2, z1), t_0);
	t_3 = min(min(z2, z1), z0);
	tmp = 0.0;
	if (t_2 <= 1e-23)
		tmp = (((sin((pi * z4)) * sin(((pi * z4) + pi))) + ((cos(((((z4 + z4) - 0.5) * pi) + (0.5 * pi))) - -1.0) * 0.5)) * z3) + ((t_1 * t_2) * t_3);
	else
		tmp = z3 + ((t_3 * t_2) * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := Block[{t$95$0 = N[Max[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Max[z2, z1], $MachinePrecision], t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[z2, z1], $MachinePrecision], t$95$0], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, If[LessEqual[t$95$2, 1e-23], N[(N[(N[(N[(N[Sin[N[(Pi * z4), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(N[(Pi * z4), $MachinePrecision] + Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Cos[N[(N[(N[(N[(z4 + z4), $MachinePrecision] - 0.5), $MachinePrecision] * Pi), $MachinePrecision] + N[(0.5 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] * z3), $MachinePrecision] + N[(N[(t$95$1 * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision], N[(z3 + N[(N[(t$95$3 * t$95$2), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 9.9999999999999996e-24

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z1 \cdot z0\right) \cdot z2} \]

      5. lower-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z1 \cdot z0\right) \cdot z2} \]

      6. *-commutative N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right)} \cdot z2 \]

      7. lower-*.f64 73.4%

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right)} \cdot z2 \]

   3. Applied rewrites 73.4%

      \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   5. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot \left(z4 + 0.5\right)\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right)} \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]
   6. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\cos \left(\pi \cdot \left(z4 + \frac{1}{2}\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \color{blue}{\left(\pi \cdot \left(z4 + \frac{1}{2}\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      3. lift-+.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot \color{blue}{\left(z4 + \frac{1}{2}\right)}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      4. distribute-lft-in N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \color{blue}{\left(\pi \cdot z4 + \pi \cdot \frac{1}{2}\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\color{blue}{\pi \cdot z4} + \pi \cdot \frac{1}{2}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      6. metadata-eval N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \pi \cdot \color{blue}{\frac{1}{2}}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      7. mult-flip N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \color{blue}{\frac{\pi}{2}}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      8. lift-PI.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      9. cos-+PI/2-rev N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\sin \left(\pi \cdot z4\right)\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      10. sin-+PI-rev N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \mathsf{PI}\left(\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      11. lower-sin.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \mathsf{PI}\left(\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      12. lift-PI.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \color{blue}{\pi}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      13. lower-+.f64 94.8%

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \color{blue}{\left(\pi \cdot z4 + \pi\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   7. Applied rewrites 94.8%

      \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \pi\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]
   8. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\color{blue}{\cos \left(\left(\pi + \pi\right) \cdot z4\right)} - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      2. cos-neg-rev N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\color{blue}{\cos \left(\mathsf{neg}\left(\left(\pi + \pi\right) \cdot z4\right)\right)} - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      3. sin-+PI/2-rev N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\color{blue}{\sin \left(\left(\mathsf{neg}\left(\left(\pi + \pi\right) \cdot z4\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)} - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{\left(\pi + \pi\right) \cdot z4}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      5. *-commutative N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{z4 \cdot \left(\pi + \pi\right)}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(z4 \cdot \color{blue}{\left(\pi + \pi\right)}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      7. distribute-lft-in N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{\left(z4 \cdot \pi + z4 \cdot \pi\right)}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      8. distribute-rgt-in N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{\pi \cdot \left(z4 + z4\right)}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\pi \cdot \color{blue}{\left(z4 + z4\right)}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      10. *-commutative N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{\left(z4 + z4\right) \cdot \pi}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      11. lift-PI.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \frac{\color{blue}{\pi}}{2}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      12. mult-flip N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \color{blue}{\pi \cdot \frac{1}{2}}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      13. metadata-eval N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \pi \cdot \color{blue}{\frac{1}{2}}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      14. *-commutative N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \color{blue}{\frac{1}{2} \cdot \pi}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      15. metadata-eval N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)} \cdot \pi\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

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

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\left(\mathsf{neg}\left(\left(z4 + z4\right) \cdot \pi\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{2} \cdot \pi\right)\right)}\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      17. distribute-neg-in N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \color{blue}{\left(\mathsf{neg}\left(\left(\left(z4 + z4\right) \cdot \pi + \frac{-1}{2} \cdot \pi\right)\right)\right)} - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      18. distribute-rgt-in N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\mathsf{neg}\left(\color{blue}{\pi \cdot \left(\left(z4 + z4\right) + \frac{-1}{2}\right)}\right)\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      19. lift-+.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\mathsf{neg}\left(\pi \cdot \color{blue}{\left(\left(z4 + z4\right) + \frac{-1}{2}\right)}\right)\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\sin \left(\mathsf{neg}\left(\color{blue}{\pi \cdot \left(\left(z4 + z4\right) + \frac{-1}{2}\right)}\right)\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   9. Applied rewrites 94.8%

      \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\color{blue}{\cos \left(\left(\left(z4 + z4\right) - 0.5\right) \cdot \pi + 0.5 \cdot \pi\right)} - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   if 9.9999999999999996e-24 < z1

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_1 := \mathsf{max}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ \mathbf{if}\;t\_3 \leq 10^{-23}:\\ \;\;\;\;\left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\cos \left(6.283185307179586 \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(t\_2 \cdot t\_3\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;z3 + \left(t\_0 \cdot t\_3\right) \cdot t\_2\\ \end{array} \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (let* ((t_0 (fmin (fmin z2 z1) z0))
       (t_1 (fmax (fmin z2 z1) z0))
       (t_2 (fmax (fmax z2 z1) t_1))
       (t_3 (fmin (fmax z2 z1) t_1)))
  (if (<= t_3 1e-23)
    (+
     (*
      (+
       (* (sin (* PI z4)) (sin (+ (* PI z4) PI)))
       (* (- (cos (* 6.283185307179586 z4)) -1.0) 0.5))
      z3)
     (* (* t_2 t_3) t_0))
    (+ z3 (* (* t_0 t_3) t_2)))))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e-23) {
		tmp = (((sin((((double) M_PI) * z4)) * sin(((((double) M_PI) * z4) + ((double) M_PI)))) + ((cos((6.283185307179586 * z4)) - -1.0) * 0.5)) * z3) + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_3) * t_2);
	}
	return tmp;
}

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e-23) {
		tmp = (((Math.sin((Math.PI * z4)) * Math.sin(((Math.PI * z4) + Math.PI))) + ((Math.cos((6.283185307179586 * z4)) - -1.0) * 0.5)) * z3) + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_3) * t_2);
	}
	return tmp;
}

Python

def code(z4, z3, z2, z1, z0):
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0
	if t_3 <= 1e-23:
		tmp = (((math.sin((math.pi * z4)) * math.sin(((math.pi * z4) + math.pi))) + ((math.cos((6.283185307179586 * z4)) - -1.0) * 0.5)) * z3) + ((t_2 * t_3) * t_0)
	else:
		tmp = z3 + ((t_0 * t_3) * t_2)
	return tmp

Julia

function code(z4, z3, z2, z1, z0)
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0.0
	if (t_3 <= 1e-23)
		tmp = Float64(Float64(Float64(Float64(sin(Float64(pi * z4)) * sin(Float64(Float64(pi * z4) + pi))) + Float64(Float64(cos(Float64(6.283185307179586 * z4)) - -1.0) * 0.5)) * z3) + Float64(Float64(t_2 * t_3) * t_0));
	else
		tmp = Float64(z3 + Float64(Float64(t_0 * t_3) * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z4, z3, z2, z1, z0)
	t_0 = min(min(z2, z1), z0);
	t_1 = max(min(z2, z1), z0);
	t_2 = max(max(z2, z1), t_1);
	t_3 = min(max(z2, z1), t_1);
	tmp = 0.0;
	if (t_3 <= 1e-23)
		tmp = (((sin((pi * z4)) * sin(((pi * z4) + pi))) + ((cos((6.283185307179586 * z4)) - -1.0) * 0.5)) * z3) + ((t_2 * t_3) * t_0);
	else
		tmp = z3 + ((t_0 * t_3) * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := Block[{t$95$0 = N[Min[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, If[LessEqual[t$95$3, 1e-23], N[(N[(N[(N[(N[Sin[N[(Pi * z4), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(N[(Pi * z4), $MachinePrecision] + Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Cos[N[(6.283185307179586 * z4), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] * z3), $MachinePrecision] + N[(N[(t$95$2 * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(z3 + N[(N[(t$95$0 * t$95$3), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 9.9999999999999996e-24

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z1 \cdot z0\right) \cdot z2} \]

      5. lower-*.f64 N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z1 \cdot z0\right) \cdot z2} \]

      6. *-commutative N/A

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right)} \cdot z2 \]

      7. lower-*.f64 73.4%

         \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right)} \cdot z2 \]

   3. Applied rewrites 73.4%

      \[\leadsto \cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   5. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot \left(z4 + 0.5\right)\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right)} \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]
   6. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\cos \left(\pi \cdot \left(z4 + \frac{1}{2}\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \color{blue}{\left(\pi \cdot \left(z4 + \frac{1}{2}\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      3. lift-+.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot \color{blue}{\left(z4 + \frac{1}{2}\right)}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      4. distribute-lft-in N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \color{blue}{\left(\pi \cdot z4 + \pi \cdot \frac{1}{2}\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\color{blue}{\pi \cdot z4} + \pi \cdot \frac{1}{2}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      6. metadata-eval N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \pi \cdot \color{blue}{\frac{1}{2}}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      7. mult-flip N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \color{blue}{\frac{\pi}{2}}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      8. lift-PI.f64 N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \cos \left(\pi \cdot z4 + \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      9. cos-+PI/2-rev N/A

         \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\sin \left(\pi \cdot z4\right)\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      10. sin-+PI-rev N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \mathsf{PI}\left(\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      11. lower-sin.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \mathsf{PI}\left(\right)\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      12. lift-PI.f64 N/A

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \color{blue}{\pi}\right) + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot \frac{1}{2}\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

      13. lower-+.f64 94.8%

          \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \color{blue}{\left(\pi \cdot z4 + \pi\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   7. Applied rewrites 94.8%

      \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \color{blue}{\sin \left(\pi \cdot z4 + \pi\right)} + \left(\cos \left(\left(\pi + \pi\right) \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   8. Evaluated real constant 94.8%

      \[\leadsto \left(\sin \left(\pi \cdot z4\right) \cdot \sin \left(\pi \cdot z4 + \pi\right) + \left(\cos \left(\color{blue}{6.283185307179586} \cdot z4\right) - -1\right) \cdot 0.5\right) \cdot z3 + \left(z0 \cdot z1\right) \cdot z2 \]

   if 9.9999999999999996e-24 < z1

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_1 := \mathsf{max}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ \mathbf{if}\;t\_3 \leq 10^{-23}:\\ \;\;\;\;z3 + \left(t\_2 \cdot t\_3\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;z3 + \left(t\_0 \cdot t\_3\right) \cdot t\_2\\ \end{array} \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (let* ((t_0 (fmin (fmin z2 z1) z0))
       (t_1 (fmax (fmin z2 z1) z0))
       (t_2 (fmax (fmax z2 z1) t_1))
       (t_3 (fmin (fmax z2 z1) t_1)))
  (if (<= t_3 1e-23)
    (+ z3 (* (* t_2 t_3) t_0))
    (+ z3 (* (* t_0 t_3) t_2)))))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e-23) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_3) * t_2);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z4, z3, z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z4
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = fmin(fmin(z2, z1), z0)
    t_1 = fmax(fmin(z2, z1), z0)
    t_2 = fmax(fmax(z2, z1), t_1)
    t_3 = fmin(fmax(z2, z1), t_1)
    if (t_3 <= 1d-23) then
        tmp = z3 + ((t_2 * t_3) * t_0)
    else
        tmp = z3 + ((t_0 * t_3) * t_2)
    end if
    code = tmp
end function

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e-23) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_3) * t_2);
	}
	return tmp;
}

Python

def code(z4, z3, z2, z1, z0):
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0
	if t_3 <= 1e-23:
		tmp = z3 + ((t_2 * t_3) * t_0)
	else:
		tmp = z3 + ((t_0 * t_3) * t_2)
	return tmp

Julia

function code(z4, z3, z2, z1, z0)
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0.0
	if (t_3 <= 1e-23)
		tmp = Float64(z3 + Float64(Float64(t_2 * t_3) * t_0));
	else
		tmp = Float64(z3 + Float64(Float64(t_0 * t_3) * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z4, z3, z2, z1, z0)
	t_0 = min(min(z2, z1), z0);
	t_1 = max(min(z2, z1), z0);
	t_2 = max(max(z2, z1), t_1);
	t_3 = min(max(z2, z1), t_1);
	tmp = 0.0;
	if (t_3 <= 1e-23)
		tmp = z3 + ((t_2 * t_3) * t_0);
	else
		tmp = z3 + ((t_0 * t_3) * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := Block[{t$95$0 = N[Min[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, If[LessEqual[t$95$3, 1e-23], N[(z3 + N[(N[(t$95$2 * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(z3 + N[(N[(t$95$0 * t$95$3), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 9.9999999999999996e-24

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      6. *-commutative N/A

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

      7. lift-*.f64 93.9%

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   6. Applied rewrites 93.9%

      \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   if 9.9999999999999996e-24 < z1

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_1 := \mathsf{max}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ \mathbf{if}\;t\_3 \leq 10^{+43}:\\ \;\;\;\;z3 + \left(t\_2 \cdot t\_3\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;z3 + \left(t\_0 \cdot t\_2\right) \cdot t\_3\\ \end{array} \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (let* ((t_0 (fmin (fmin z2 z1) z0))
       (t_1 (fmax (fmin z2 z1) z0))
       (t_2 (fmax (fmax z2 z1) t_1))
       (t_3 (fmin (fmax z2 z1) t_1)))
  (if (<= t_3 1e+43)
    (+ z3 (* (* t_2 t_3) t_0))
    (+ z3 (* (* t_0 t_2) t_3)))))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e+43) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_2) * t_3);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z4, z3, z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z4
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = fmin(fmin(z2, z1), z0)
    t_1 = fmax(fmin(z2, z1), z0)
    t_2 = fmax(fmax(z2, z1), t_1)
    t_3 = fmin(fmax(z2, z1), t_1)
    if (t_3 <= 1d+43) then
        tmp = z3 + ((t_2 * t_3) * t_0)
    else
        tmp = z3 + ((t_0 * t_2) * t_3)
    end if
    code = tmp
end function

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 1e+43) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = z3 + ((t_0 * t_2) * t_3);
	}
	return tmp;
}

Python

def code(z4, z3, z2, z1, z0):
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0
	if t_3 <= 1e+43:
		tmp = z3 + ((t_2 * t_3) * t_0)
	else:
		tmp = z3 + ((t_0 * t_2) * t_3)
	return tmp

Julia

function code(z4, z3, z2, z1, z0)
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0.0
	if (t_3 <= 1e+43)
		tmp = Float64(z3 + Float64(Float64(t_2 * t_3) * t_0));
	else
		tmp = Float64(z3 + Float64(Float64(t_0 * t_2) * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z4, z3, z2, z1, z0)
	t_0 = min(min(z2, z1), z0);
	t_1 = max(min(z2, z1), z0);
	t_2 = max(max(z2, z1), t_1);
	t_3 = min(max(z2, z1), t_1);
	tmp = 0.0;
	if (t_3 <= 1e+43)
		tmp = z3 + ((t_2 * t_3) * t_0);
	else
		tmp = z3 + ((t_0 * t_2) * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := Block[{t$95$0 = N[Min[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, If[LessEqual[t$95$3, 1e+43], N[(z3 + N[(N[(t$95$2 * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(z3 + N[(N[(t$95$0 * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 1e43

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      6. *-commutative N/A

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

      7. lift-*.f64 93.9%

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   6. Applied rewrites 93.9%

      \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   if 1e43 < z1

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      5. associate-*r* N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z0\right) \cdot z1} \]

      6. lower-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z0\right) \cdot z1} \]

      7. lower-*.f64 93.8%

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z0\right)} \cdot z1 \]

   6. Applied rewrites 93.8%

      \[\leadsto z3 + \color{blue}{\left(z2 \cdot z0\right) \cdot z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_1 := \mathsf{max}\left(\mathsf{min}\left(z2, z1\right), z0\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z2, z1\right), t\_1\right)\\ \mathbf{if}\;t\_3 \leq 5.6 \cdot 10^{+88}:\\ \;\;\;\;z3 + \left(t\_2 \cdot t\_3\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \left(t\_3 \cdot t\_0\right)\\ \end{array} \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (let* ((t_0 (fmin (fmin z2 z1) z0))
       (t_1 (fmax (fmin z2 z1) z0))
       (t_2 (fmax (fmax z2 z1) t_1))
       (t_3 (fmin (fmax z2 z1) t_1)))
  (if (<= t_3 5.6e+88)
    (+ z3 (* (* t_2 t_3) t_0))
    (* t_2 (* t_3 t_0)))))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 5.6e+88) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = t_2 * (t_3 * t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z4, z3, z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z4
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = fmin(fmin(z2, z1), z0)
    t_1 = fmax(fmin(z2, z1), z0)
    t_2 = fmax(fmax(z2, z1), t_1)
    t_3 = fmin(fmax(z2, z1), t_1)
    if (t_3 <= 5.6d+88) then
        tmp = z3 + ((t_2 * t_3) * t_0)
    else
        tmp = t_2 * (t_3 * t_0)
    end if
    code = tmp
end function

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	double t_0 = fmin(fmin(z2, z1), z0);
	double t_1 = fmax(fmin(z2, z1), z0);
	double t_2 = fmax(fmax(z2, z1), t_1);
	double t_3 = fmin(fmax(z2, z1), t_1);
	double tmp;
	if (t_3 <= 5.6e+88) {
		tmp = z3 + ((t_2 * t_3) * t_0);
	} else {
		tmp = t_2 * (t_3 * t_0);
	}
	return tmp;
}

Python

def code(z4, z3, z2, z1, z0):
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0
	if t_3 <= 5.6e+88:
		tmp = z3 + ((t_2 * t_3) * t_0)
	else:
		tmp = t_2 * (t_3 * t_0)
	return tmp

Julia

function code(z4, z3, z2, z1, z0)
	t_0 = fmin(fmin(z2, z1), z0)
	t_1 = fmax(fmin(z2, z1), z0)
	t_2 = fmax(fmax(z2, z1), t_1)
	t_3 = fmin(fmax(z2, z1), t_1)
	tmp = 0.0
	if (t_3 <= 5.6e+88)
		tmp = Float64(z3 + Float64(Float64(t_2 * t_3) * t_0));
	else
		tmp = Float64(t_2 * Float64(t_3 * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z4, z3, z2, z1, z0)
	t_0 = min(min(z2, z1), z0);
	t_1 = max(min(z2, z1), z0);
	t_2 = max(max(z2, z1), t_1);
	t_3 = min(max(z2, z1), t_1);
	tmp = 0.0;
	if (t_3 <= 5.6e+88)
		tmp = z3 + ((t_2 * t_3) * t_0);
	else
		tmp = t_2 * (t_3 * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := Block[{t$95$0 = N[Min[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Min[z2, z1], $MachinePrecision], z0], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z2, z1], $MachinePrecision], t$95$1], $MachinePrecision]}, If[LessEqual[t$95$3, 5.6e+88], N[(z3 + N[(N[(t$95$2 * t$95$3), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z1 < 5.5999999999999998e88

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z4 around 0

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   3. Step-by-step derivation

   4. Applied rewrites 93.5%

      \[\leadsto \color{blue}{z3} + \left(z2 \cdot z1\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right) \cdot z0} \]

      2. lift-*.f64 N/A

         \[\leadsto z3 + \color{blue}{\left(z2 \cdot z1\right)} \cdot z0 \]

      3. associate-*l* N/A

         \[\leadsto z3 + \color{blue}{z2 \cdot \left(z1 \cdot z0\right)} \]

      4. *-commutative N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto z3 + z2 \cdot \color{blue}{\left(z0 \cdot z1\right)} \]

      6. *-commutative N/A

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

      7. lift-*.f64 93.9%

         \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   6. Applied rewrites 93.9%

      \[\leadsto z3 + \color{blue}{\left(z0 \cdot z1\right) \cdot z2} \]

   if 5.5999999999999998e88 < z1

   1. Initial program 73.1%

      \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

   2. Taylor expanded in z3 around 0

      \[\leadsto \color{blue}{z0 \cdot \left(z1 \cdot z2\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

      2. lower-*.f64 47.3%

         \[\leadsto z0 \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

   4. Applied rewrites 47.3%

      \[\leadsto \color{blue}{z0 \cdot \left(z1 \cdot z2\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 47.3% accurate, 11.5× speedup

Math

\[z0 \cdot \left(z1 \cdot z2\right) \]

FPCore

(FPCore (z4 z3 z2 z1 z0)
  :precision binary64
  (* z0 (* z1 z2)))

C

double code(double z4, double z3, double z2, double z1, double z0) {
	return z0 * (z1 * z2);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z4, z3, z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z4
    real(8), intent (in) :: z3
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = z0 * (z1 * z2)
end function

Java

public static double code(double z4, double z3, double z2, double z1, double z0) {
	return z0 * (z1 * z2);
}

Python

def code(z4, z3, z2, z1, z0):
	return z0 * (z1 * z2)

Julia

function code(z4, z3, z2, z1, z0)
	return Float64(z0 * Float64(z1 * z2))
end

MATLAB

function tmp = code(z4, z3, z2, z1, z0)
	tmp = z0 * (z1 * z2);
end

Wolfram

code[z4_, z3_, z2_, z1_, z0_] := N[(z0 * N[(z1 * z2), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.1%

   \[\cos \left(\left(\pi + \pi\right) \cdot z4\right) \cdot z3 + \left(z2 \cdot z1\right) \cdot z0 \]

2. Taylor expanded in z3 around 0

   \[\leadsto \color{blue}{z0 \cdot \left(z1 \cdot z2\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z0 \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

   2. lower-*.f64 47.3%

      \[\leadsto z0 \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

4. Applied rewrites 47.3%

   \[\leadsto \color{blue}{z0 \cdot \left(z1 \cdot z2\right)} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025256 
(FPCore (z4 z3 z2 z1 z0)
  :name "(+ (* (cos (* (+ PI PI) z4)) z3) (* (* z2 z1) z0))"
  :precision binary64
  (+ (* (cos (* (+ PI PI) z4)) z3) (* (* z2 z1) z0)))