Kahan p13 Example 2

Average Error: 0.0 → 0.0

Time: 16.1s

Precision: binary64

Cost: 14528

Math

\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \]

↓

\[\begin{array}{l} t_1 := \frac{2}{1 + t}\\ t_2 := t_1 + -4\\ \frac{\mathsf{fma}\left(t_1, t_2, 5\right)}{\mathsf{fma}\left(t_1, t_2, 6\right)} \end{array} \]

FPCore

(FPCore (t)
 :precision binary64
 (/
  (+
   1.0
   (*
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))
  (+
   2.0
   (*
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))
    (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))

↓

(FPCore (t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (+ 1.0 t))) (t_2 (+ t_1 -4.0)))
   (/ (fma t_1 t_2 5.0) (fma t_1 t_2 6.0))))

C

double code(double t) {
	return (1.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))))) / (2.0 + ((2.0 - ((2.0 / t) / (1.0 + (1.0 / t)))) * (2.0 - ((2.0 / t) / (1.0 + (1.0 / t))))));
}

↓

double code(double t) {
	double t_1 = 2.0 / (1.0 + t);
	double t_2 = t_1 + -4.0;
	return fma(t_1, t_2, 5.0) / fma(t_1, t_2, 6.0);
}

Julia

function code(t)
	return Float64(Float64(1.0 + Float64(Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))) * Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))))) / Float64(2.0 + Float64(Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))) * Float64(2.0 - Float64(Float64(2.0 / t) / Float64(1.0 + Float64(1.0 / t)))))))
end

↓

function code(t)
	t_1 = Float64(2.0 / Float64(1.0 + t))
	t_2 = Float64(t_1 + -4.0)
	return Float64(fma(t_1, t_2, 5.0) / fma(t_1, t_2, 6.0))
end

Wolfram

code[t_] := N[(N[(1.0 + N[(N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[(N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 - N[(N[(2.0 / t), $MachinePrecision] / N[(1.0 + N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[t_] := Block[{t$95$1 = N[(2.0 / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + -4.0), $MachinePrecision]}, N[(N[(t$95$1 * t$95$2 + 5.0), $MachinePrecision] / N[(t$95$1 * t$95$2 + 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 0.0

   \[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{2}{1 + t}, \frac{2}{1 + t} + -4, 5\right)}{\mathsf{fma}\left(\frac{2}{1 + t}, \frac{2}{1 + t} + -4, 6\right)}} \]
   Proof
   (/.f64 (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 2 (+.f64 (Rewrite<= lft-mult-inverse_binary64 (*.f64 (/.f64 1 t) t)) t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 15 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 2 (+.f64 (*.f64 (/.f64 1 t) t) (Rewrite<= *-lft-identity_binary64 (*.f64 1 t)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 2 (Rewrite=> distribute-rgt-out_binary64 (*.f64 t (+.f64 (/.f64 1 t) 1)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 2 (*.f64 t (Rewrite<= +-commutative_binary64 (+.f64 1 (/.f64 1 t))))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 15 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (+.f64 (Rewrite<= lft-mult-inverse_binary64 (*.f64 (/.f64 1 t) t)) t)) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 15 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (+.f64 (*.f64 (/.f64 1 t) t) (Rewrite<= *-lft-identity_binary64 (*.f64 1 t)))) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (Rewrite=> distribute-rgt-out_binary64 (*.f64 t (+.f64 (/.f64 1 t) 1)))) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (*.f64 t (Rewrite<= +-commutative_binary64 (+.f64 1 (/.f64 1 t))))) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -4) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 2 points increase in error, 15 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (Rewrite<= metadata-eval (+.f64 -2 -2))) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= metadata-eval (neg.f64 2)) -2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (neg.f64 2) (Rewrite<= metadata-eval (neg.f64 2)))) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (neg.f64 2)) (neg.f64 2))) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 1 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (+.f64 (Rewrite=> metadata-eval -2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (+.f64 (Rewrite<= metadata-eval (-.f64 0 2)) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1)) (neg.f64 2)) 5) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2)) (Rewrite<= metadata-eval (+.f64 1 4))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2)) (+.f64 1 (Rewrite<= metadata-eval (*.f64 2 2)))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2))) (+.f64 1 (*.f64 2 2)))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 1 points increase in error, 2 points decrease in error
   (/.f64 (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 2 points decrease in error
   (/.f64 (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (*.f64 -1 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= neg-mul-1_binary64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (neg.f64 (*.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (Rewrite<= distribute-rgt-neg-out_binary64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) (+.f64 1 (*.f64 2 2))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 1 (Rewrite=> metadata-eval 4))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite=> metadata-eval 5)) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite<= metadata-eval (+.f64 4 1))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= metadata-eval (*.f64 2 2)) 1)) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 2 2)) 1)) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 2 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 2)))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 7 points increase in error, 1 points decrease in error
   (/.f64 (+.f64 (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 2))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (Rewrite<= distribute-lft-in_binary64 (*.f64 2 (+.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) 2)))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (Rewrite<= sub-neg_binary64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (+.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) 2))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 2 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= +-commutative_binary64 (+.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= sub-neg_binary64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) 1) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) (fma.f64 (/.f64 2 (+.f64 1 t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 2 (+.f64 (Rewrite<= lft-mult-inverse_binary64 (*.f64 (/.f64 1 t) t)) t)) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 15 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 2 (+.f64 (*.f64 (/.f64 1 t) t) (Rewrite<= *-lft-identity_binary64 (*.f64 1 t)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 2 (Rewrite=> distribute-rgt-out_binary64 (*.f64 t (+.f64 (/.f64 1 t) 1)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 2 (*.f64 t (Rewrite<= +-commutative_binary64 (+.f64 1 (/.f64 1 t))))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (+.f64 (/.f64 2 (+.f64 1 t)) -4) 6)): 2 points increase in error, 15 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (+.f64 (Rewrite<= lft-mult-inverse_binary64 (*.f64 (/.f64 1 t) t)) t)) -4) 6)): 15 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (+.f64 (*.f64 (/.f64 1 t) t) (Rewrite<= *-lft-identity_binary64 (*.f64 1 t)))) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (Rewrite=> distribute-rgt-out_binary64 (*.f64 t (+.f64 (/.f64 1 t) 1)))) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 2 (*.f64 t (Rewrite<= +-commutative_binary64 (+.f64 1 (/.f64 1 t))))) -4) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -4) 6)): 0 points increase in error, 17 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (Rewrite<= metadata-eval (+.f64 -2 -2))) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= metadata-eval (neg.f64 2)) -2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (neg.f64 2) (Rewrite<= metadata-eval (neg.f64 2)))) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (neg.f64 2)) (neg.f64 2))) 6)): 0 points increase in error, 1 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (+.f64 (Rewrite=> metadata-eval -2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (+.f64 (Rewrite<= metadata-eval (-.f64 0 2)) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1)) (neg.f64 2)) 6)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2)) (Rewrite<= metadata-eval (+.f64 2 4)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (fma.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2)) (+.f64 2 (Rewrite<= metadata-eval (*.f64 2 2))))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (neg.f64 2))) (+.f64 2 (*.f64 2 2))))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) -1) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 2 (*.f64 2 2)))): 2 points increase in error, 2 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (*.f64 -1 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 2 (*.f64 2 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= neg-mul-1_binary64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 (neg.f64 2) (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 2 (*.f64 2 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 2 (*.f64 2 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (neg.f64 (*.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) (+.f64 2 (*.f64 2 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (Rewrite<= distribute-rgt-neg-out_binary64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) (+.f64 2 (*.f64 2 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 2 (Rewrite=> metadata-eval 4)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite=> metadata-eval 6))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite<= metadata-eval (+.f64 4 2)))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= metadata-eval (*.f64 2 2)) 2))): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (*.f64 2 2)) 2))): 1 points increase in error, 1 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (+.f64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 2)))) 2)): 0 points increase in error, 6 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (*.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 2))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (Rewrite<= distribute-lft-in_binary64 (*.f64 2 (+.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) 2)))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (+.f64 (*.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))) (*.f64 2 (Rewrite<= sub-neg_binary64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (+.f64 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) 2))) 2)): 0 points increase in error, 2 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= +-commutative_binary64 (+.f64 2 (neg.f64 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t))))))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (+.f64 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (Rewrite<= sub-neg_binary64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) 2)): 0 points increase in error, 0 points decrease in error
   (/.f64 (+.f64 1 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))) (Rewrite<= +-commutative_binary64 (+.f64 2 (*.f64 (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))) (-.f64 2 (/.f64 (/.f64 2 t) (+.f64 1 (/.f64 1 t)))))))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

   \[\leadsto \frac{\mathsf{fma}\left(\frac{2}{1 + t}, \frac{2}{1 + t} + -4, 5\right)}{\mathsf{fma}\left(\frac{2}{1 + t}, \frac{2}{1 + t} + -4, 6\right)} \]

Alternatives

Alternative 1
Error	0.0
Cost	3264

\[\begin{array}{l} t_1 := 2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\\ t_2 := t_1 \cdot t_1\\ \frac{1 + t_2}{2 + t_2} \end{array} \]

Alternative 2
Error	0.3
Cost	2888

\[\begin{array}{l} t_1 := \left(\frac{\frac{0.037037037037037035}{t}}{t} + \left(0.8333333333333334 + \frac{\frac{0.04938271604938271}{t \cdot t}}{t}\right)\right) + \frac{1}{t} \cdot -0.2222222222222222\\ t_2 := 2 + \frac{\frac{-2}{t}}{1 + \frac{1}{t}}\\ \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;\frac{1 + t_2 \cdot t_2}{2 + \left(t \cdot t\right) \cdot \left(t \cdot \left(t \cdot 12 + -8\right) + 4\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	0.3
Cost	1736

\[\begin{array}{l} t_1 := \left(\frac{\frac{0.037037037037037035}{t}}{t} + \left(0.8333333333333334 + \frac{\frac{0.04938271604938271}{t \cdot t}}{t}\right)\right) + \frac{1}{t} \cdot -0.2222222222222222\\ t_2 := 4 + t \cdot -8\\ \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;\frac{1 + t \cdot \left(t \cdot t_2\right)}{2 + \left(t \cdot t\right) \cdot t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	0.4
Cost	1608

\[\begin{array}{l} t_1 := \left(\frac{\frac{0.037037037037037035}{t}}{t} + \left(0.8333333333333334 + \frac{\frac{0.04938271604938271}{t \cdot t}}{t}\right)\right) + \frac{1}{t} \cdot -0.2222222222222222\\ \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;\frac{1 + t \cdot \left(t \cdot \left(4 + t \cdot -8\right)\right)}{2 + t \cdot \left(t \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	0.4
Cost	1480

\[\begin{array}{l} \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;\frac{0.037037037037037035}{t \cdot t} + \left(0.8333333333333334 + \frac{-0.2222222222222222}{t}\right)\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;\frac{1 + t \cdot \left(t \cdot \left(4 + t \cdot -8\right)\right)}{2 + t \cdot \left(t \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{\frac{0.037037037037037035}{t} + -0.2222222222222222}{t}\\ \end{array} \]

Alternative 6
Error	0.5
Cost	840

\[\begin{array}{l} t_1 := 0.8333333333333334 + \frac{\frac{0.037037037037037035}{t} + -0.2222222222222222}{t}\\ \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	0.5
Cost	840

\[\begin{array}{l} \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;\frac{0.037037037037037035}{t \cdot t} + \left(0.8333333333333334 + \frac{-0.2222222222222222}{t}\right)\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{\frac{0.037037037037037035}{t} + -0.2222222222222222}{t}\\ \end{array} \]

Alternative 8
Error	0.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;\left(1 + \frac{-0.2222222222222222}{t}\right) + -0.16666666666666666\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;1 + \left(-0.16666666666666666 - \frac{0.2222222222222222}{t}\right)\\ \end{array} \]

Alternative 9
Error	0.6
Cost	584

\[\begin{array}{l} t_1 := 0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	0.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;\left(1 + \frac{-0.2222222222222222}{t}\right) + -0.16666666666666666\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334 + \frac{-0.2222222222222222}{t}\\ \end{array} \]

Alternative 11
Error	0.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -10.621655339931833:\\ \;\;\;\;0.8333333333333334\\ \mathbf{elif}\;t \leq 0.004648620581173463:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;0.8333333333333334\\ \end{array} \]

Alternative 12
Error	26.4
Cost	64

\[0.8333333333333334 \]

Reproduce

herbie shell --seed 2022308 
(FPCore (t)
  :name "Kahan p13 Example 2"
  :precision binary64
  (/ (+ 1.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))) (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t))))))))