Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1

Average Error: 45.8 → 42.9

Time: 24.3s

Precision: binary64

Cost: 48964

Math

\[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

↓

\[\begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(z \cdot t\right) \cdot \left(y \cdot 0.125\right)\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(\left(\cos t_1 \cdot \cos t_2 - \sin t_1 \cdot \sin t_2\right) \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + \frac{a}{8}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* z t) (* y 0.125))))
   (if (<=
        (*
         (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
         (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        5e+280)
     (*
      x
      (*
       (- (* (cos t_1) (cos t_2)) (* (sin t_1) (sin t_2)))
       (cos (* (* t b) (+ 0.0625 (/ a 8.0))))))
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (z * t) * (y * 0.125);
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+280) {
		tmp = x * (((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2))) * cos(((t * b) * (0.0625 + (a / 8.0)))));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos((((((a * 2.0d0) + 1.0d0) * b) * t) / 16.0d0))
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (z * t) * (y * 0.125d0)
    if (((x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos(((t * ((1.0d0 + (2.0d0 * a)) * b)) / 16.0d0))) <= 5d+280) then
        tmp = x * (((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2))) * cos(((t * b) * (0.0625d0 + (a / 8.0d0)))))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (z * t) * (y * 0.125);
	double tmp;
	if (((x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+280) {
		tmp = x * (((Math.cos(t_1) * Math.cos(t_2)) - (Math.sin(t_1) * Math.sin(t_2))) * Math.cos(((t * b) * (0.0625 + (a / 8.0)))));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0))

↓

def code(x, y, z, t, a, b):
	t_1 = 0.0625 * (z * t)
	t_2 = (z * t) * (y * 0.125)
	tmp = 0
	if ((x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+280:
		tmp = x * (((math.cos(t_1) * math.cos(t_2)) - (math.sin(t_1) * math.sin(t_2))) * math.cos(((t * b) * (0.0625 + (a / 8.0)))))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(z * t) * Float64(y * 0.125))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+280)
		tmp = Float64(x * Float64(Float64(Float64(cos(t_1) * cos(t_2)) - Float64(sin(t_1) * sin(t_2))) * cos(Float64(Float64(t * b) * Float64(0.0625 + Float64(a / 8.0))))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.0625 * (z * t);
	t_2 = (z * t) * (y * 0.125);
	tmp = 0.0;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+280)
		tmp = x * (((cos(t_1) * cos(t_2)) - (sin(t_1) * sin(t_2))) * cos(((t * b) * (0.0625 + (a / 8.0)))));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * N[(y * 0.125), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+280], N[(x * N[(N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * b), $MachinePrecision] * N[(0.0625 + N[(a / 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Target

Original	45.8
Target	44.0
Herbie	42.9

\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right) \]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000002e280

   1. Initial program 33.5

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

   2. Simplified 33.5

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(\left(t \cdot b\right) \cdot \left(\frac{a}{8} + 0.0625\right)\right)\right)} \]
      Proof
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 1/16 (/.f64 y 8)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (Rewrite<= metadata-eval (/.f64 1 16)) (/.f64 y 8)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (/.f64 y (Rewrite<= metadata-eval (/.f64 16 2)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y 2) 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y 2) 16)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1 (*.f64 y 2)) 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-/l*_binary64 (/.f64 1 (/.f64 16 (*.f64 y 2))))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 1 16) (*.f64 y 2)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 y 2) (/.f64 1 16)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (Rewrite=> distribute-rgt1-in_binary64 (*.f64 (+.f64 (*.f64 y 2) 1) (/.f64 1 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (+.f64 (*.f64 y 2) 1))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (*.f64 z t) (/.f64 1 16)) (+.f64 (*.f64 y 2) 1)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 1 points increase in error, 37 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (*.f64 z t))) (+.f64 (*.f64 y 2) 1))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 16 (*.f64 z t)))) (+.f64 (*.f64 y 2) 1))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 1 (+.f64 (*.f64 y 2) 1)) (/.f64 16 (*.f64 z t))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1 (/.f64 (+.f64 (*.f64 y 2) 1) (/.f64 16 (*.f64 z t)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 1 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (*.f64 y 2) 1) (*.f64 z t)) 16)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 1 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t)) 16))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 b t)) (+.f64 (/.f64 a 8) 1/16))))): 6 points increase in error, 32 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (/.f64 a (Rewrite<= metadata-eval (/.f64 16 2))) 1/16))))): 15 points increase in error, 23 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a 2) 16)) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (/.f64 (*.f64 a 2) 16) (Rewrite<= metadata-eval (/.f64 1 16))))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite=> *-commutative_binary64 (*.f64 (+.f64 (/.f64 (*.f64 a 2) 16) (/.f64 1 16)) (*.f64 b t)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 a 2) 16))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1 (*.f64 a 2)) 16)) (/.f64 1 16)) (*.f64 b t))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-/l*_binary64 (/.f64 1 (/.f64 16 (*.f64 a 2)))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 1 16) (*.f64 a 2))) (/.f64 1 16)) (*.f64 b t))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 a 2) (/.f64 1 16))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite=> distribute-lft1-in_binary64 (*.f64 (+.f64 (*.f64 a 2) 1) (/.f64 1 16))) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (+.f64 (*.f64 a 2) 1))) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 16) (*.f64 (+.f64 (*.f64 a 2) 1) (*.f64 b t))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (/.f64 1 16) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t)))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 16 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t))))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t)) 16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))))): 0 points increase in error, 38 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))): 38 points increase in error, 0 points decrease in error

   3. Applied egg-rr 33.4

      \[\leadsto x \cdot \left(\color{blue}{\left(\cos \left(t \cdot \left(z \cdot 0.0625\right)\right) \cdot \cos \left(t \cdot \left(z \cdot \left(y \cdot 0.125\right)\right)\right) - \sin \left(t \cdot \left(z \cdot 0.0625\right)\right) \cdot \sin \left(t \cdot \left(z \cdot \left(y \cdot 0.125\right)\right)\right)\right)} \cdot \cos \left(\left(t \cdot b\right) \cdot \left(\frac{a}{8} + 0.0625\right)\right)\right) \]

   4. Simplified 33.5

      \[\leadsto x \cdot \left(\color{blue}{\left(\cos \left(0.0625 \cdot \left(t \cdot z\right)\right) \cdot \cos \left(\left(t \cdot z\right) \cdot \left(0.125 \cdot y\right)\right) - \sin \left(0.0625 \cdot \left(t \cdot z\right)\right) \cdot \sin \left(\left(t \cdot z\right) \cdot \left(0.125 \cdot y\right)\right)\right)} \cdot \cos \left(\left(t \cdot b\right) \cdot \left(\frac{a}{8} + 0.0625\right)\right)\right) \]
      Proof
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 1/16 (*.f64 t z))) (cos.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y)))) (*.f64 (sin.f64 (*.f64 1/16 (*.f64 t z))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 t z) 1/16))) (cos.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y)))) (*.f64 (sin.f64 (*.f64 1/16 (*.f64 t z))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 9 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z 1/16)))) (cos.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y)))) (*.f64 (sin.f64 (*.f64 1/16 (*.f64 t z))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 9 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (*.f64 (*.f64 t z) (Rewrite<= *-commutative_binary64 (*.f64 y 1/8))))) (*.f64 (sin.f64 (*.f64 1/16 (*.f64 t z))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 9 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z (*.f64 y 1/8)))))) (*.f64 (sin.f64 (*.f64 1/16 (*.f64 t z))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 9 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (*.f64 t (*.f64 z (*.f64 y 1/8))))) (*.f64 (sin.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 t z) 1/16))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 9 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (*.f64 t (*.f64 z (*.f64 y 1/8))))) (*.f64 (sin.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z 1/16)))) (sin.f64 (*.f64 (*.f64 t z) (*.f64 1/8 y))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 9 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (*.f64 t (*.f64 z (*.f64 y 1/8))))) (*.f64 (sin.f64 (*.f64 t (*.f64 z 1/16))) (sin.f64 (*.f64 (*.f64 t z) (Rewrite<= *-commutative_binary64 (*.f64 y 1/8)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 9 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (-.f64 (*.f64 (cos.f64 (*.f64 t (*.f64 z 1/16))) (cos.f64 (*.f64 t (*.f64 z (*.f64 y 1/8))))) (*.f64 (sin.f64 (*.f64 t (*.f64 z 1/16))) (sin.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z (*.f64 y 1/8))))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error

   if 5.0000000000000002e280 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 62.9

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

   2. Simplified 62.9

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right) \cdot z}{\frac{16}{t}}\right) \cdot \cos \left(\frac{\mathsf{fma}\left(a, 2, 1\right) \cdot b}{\frac{16}{t}}\right)\right)} \]
      Proof
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 1/16 (/.f64 y 8)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (Rewrite<= metadata-eval (/.f64 1 16)) (/.f64 y 8)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (/.f64 y (Rewrite<= metadata-eval (/.f64 16 2)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y 2) 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y 2) 16)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1 (*.f64 y 2)) 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-/l*_binary64 (/.f64 1 (/.f64 16 (*.f64 y 2))))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 1 16) (*.f64 y 2)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (+.f64 (/.f64 1 16) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 y 2) (/.f64 1 16)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (Rewrite=> distribute-rgt1-in_binary64 (*.f64 (+.f64 (*.f64 y 2) 1) (/.f64 1 16))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (*.f64 z t) (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (+.f64 (*.f64 y 2) 1))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (*.f64 z t) (/.f64 1 16)) (+.f64 (*.f64 y 2) 1)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 1 points increase in error, 37 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (*.f64 z t))) (+.f64 (*.f64 y 2) 1))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 16 (*.f64 z t)))) (+.f64 (*.f64 y 2) 1))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 1 (+.f64 (*.f64 y 2) 1)) (/.f64 16 (*.f64 z t))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1 (/.f64 (+.f64 (*.f64 y 2) 1) (/.f64 16 (*.f64 z t)))))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 1 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (*.f64 y 2) 1) (*.f64 z t)) 16)))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (*.f64 1 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t)) 16))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (*.f64 (*.f64 t b) (+.f64 (/.f64 a 8) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 b t)) (+.f64 (/.f64 a 8) 1/16))))): 6 points increase in error, 32 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (/.f64 a (Rewrite<= metadata-eval (/.f64 16 2))) 1/16))))): 15 points increase in error, 23 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a 2) 16)) 1/16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (*.f64 b t) (+.f64 (/.f64 (*.f64 a 2) 16) (Rewrite<= metadata-eval (/.f64 1 16))))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite=> *-commutative_binary64 (*.f64 (+.f64 (/.f64 (*.f64 a 2) 16) (/.f64 1 16)) (*.f64 b t)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 a 2) 16))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1 (*.f64 a 2)) 16)) (/.f64 1 16)) (*.f64 b t))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-/l*_binary64 (/.f64 1 (/.f64 16 (*.f64 a 2)))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 1 16) (*.f64 a 2))) (/.f64 1 16)) (*.f64 b t))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 a 2) (/.f64 1 16))) (/.f64 1 16)) (*.f64 b t))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite=> distribute-lft1-in_binary64 (*.f64 (+.f64 (*.f64 a 2) 1) (/.f64 1 16))) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 16) (+.f64 (*.f64 a 2) 1))) (*.f64 b t))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 16) (*.f64 (+.f64 (*.f64 a 2) 1) (*.f64 b t))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (*.f64 (/.f64 1 16) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t)))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 16 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t))))))): 0 points increase in error, 38 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t)) 16))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))))): 38 points increase in error, 0 points decrease in error
      (*.f64 x (*.f64 (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16)) (cos.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))))): 0 points increase in error, 38 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))): 38 points increase in error, 0 points decrease in error

   3. Taylor expanded in b around 0 60.3

      \[\leadsto x \cdot \left(\cos \left(\frac{\mathsf{fma}\left(y, 2, 1\right) \cdot z}{\frac{16}{t}}\right) \cdot \color{blue}{1}\right) \]

   4. Taylor expanded in z around 0 56.1

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(\left(\cos \left(0.0625 \cdot \left(z \cdot t\right)\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(y \cdot 0.125\right)\right) - \sin \left(0.0625 \cdot \left(z \cdot t\right)\right) \cdot \sin \left(\left(z \cdot t\right) \cdot \left(y \cdot 0.125\right)\right)\right) \cdot \cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + \frac{a}{8}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternatives

Alternative 1
Error	43.0
Cost	41412

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(\cos \left(\frac{z}{\frac{16}{t}} \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \cos \left(\frac{b \cdot \mathsf{fma}\left(a, 2, 1\right)}{\frac{16}{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	42.9
Cost	28612

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+280}:\\ \;\;\;\;x \cdot \left(\cos \left(\left(t \cdot b\right) \cdot \left(0.0625 + \frac{a}{8}\right)\right) \cdot \cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	44.5
Cost	13248

\[x \cdot \cos \left(\left(z \cdot t\right) \cdot \sqrt[3]{0.000244140625}\right) \]

Alternative 4
Error	44.5
Cost	6848

\[x \cdot \cos \left(\frac{z}{\frac{16}{t}}\right) \]

Alternative 5
Error	43.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))