?

Average Error: 0.1 → 0.1
Time: 1.2min
Precision: binary64
Cost: 7360

?

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
↓
\[\left(c + x \cdot y\right) - \mathsf{fma}\left(b, a \cdot 0.25, \left(z \cdot t\right) \cdot -0.0625\right) \]
(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))
↓
(FPCore (x y z t a b c)
 :precision binary64
 (- (+ c (* x y)) (fma b (* a 0.25) (* (* z t) -0.0625))))
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (c + (x * y)) - fma(b, (a * 0.25), ((z * t) * -0.0625));
}

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end
↓
function code(x, y, z, t, a, b, c)
	return Float64(Float64(c + Float64(x * y)) - fma(b, Float64(a * 0.25), Float64(Float64(z * t) * -0.0625)))
end

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(a * 0.25), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(c + x \cdot y\right) - \mathsf{fma}\left(b, a \cdot 0.25, \left(z \cdot t\right) \cdot -0.0625\right)

Error?

Derivation?

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

  2. Applied egg-rr0.1

    \[\leadsto \color{blue}{\left(c + x \cdot y\right) - \mathsf{fma}\left(b, a \cdot 0.25, \left(z \cdot t\right) \cdot -0.0625\right)} \]

Alternatives

Alternative 1
Error22.6
Cost2396
\[\begin{array}{l} t_1 := y \cdot x - 0.25 \cdot \left(a \cdot b\right)\\ t_2 := \left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+122}:\\ \;\;\;\;c - \left(0.25 \cdot a\right) \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot x - -0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-173}:\\ \;\;\;\;y \cdot x + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25 + c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error6.5
Cost2132
\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := 0.25 \cdot \left(a \cdot b\right)\\ t_3 := \left(c + y \cdot x\right) - t_2\\ t_4 := \left(c + t_1\right) - t_2\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+150}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-52}:\\ \;\;\;\;\left(y \cdot x + t_1\right) + c\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+67}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 3
Error43.4
Cost2036
\[\begin{array}{l} t_1 := \left(-0.25 \cdot a\right) \cdot b\\ t_2 := \left(0.0625 \cdot t\right) \cdot z\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-98}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-286}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-247}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-112}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 4.75 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 0.002:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error21.3
Cost2008
\[\begin{array}{l} t_1 := \left(t \cdot z\right) \cdot 0.0625 + c\\ t_2 := y \cdot x + c\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+118}:\\ \;\;\;\;c - \left(0.25 \cdot a\right) \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot x - -0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25 + c\\ \end{array} \]
Alternative 5
Error21.1
Cost1488
\[\begin{array}{l} t_1 := y \cdot x + c\\ t_2 := \left(a \cdot b\right) \cdot -0.25 + c\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error21.1
Cost1488
\[\begin{array}{l} t_1 := y \cdot x + c\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+118}:\\ \;\;\;\;c - \left(0.25 \cdot a\right) \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25 + c\\ \end{array} \]
Alternative 7
Error10.4
Cost1224
\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+118}:\\ \;\;\;\;c - \left(0.25 \cdot a\right) \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right) + c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]
Alternative 8
Error9.5
Cost1224
\[\begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := t_1 - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 10^{+32}:\\ \;\;\;\;\left(y \cdot x + t_1\right) + c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error6.2
Cost1224
\[\begin{array}{l} t_1 := \left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-52}:\\ \;\;\;\;\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right) + c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error31.0
Cost1112
\[\begin{array}{l} t_1 := \left(-0.25 \cdot a\right) \cdot b\\ t_2 := y \cdot x + c\\ \mathbf{if}\;c \leq -1.1:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-61}:\\ \;\;\;\;\left(0.0625 \cdot t\right) \cdot z\\ \mathbf{elif}\;c \leq 3700000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 11
Error0.1
Cost1088
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(a \cdot 0.25\right) \cdot b\right) + c \]
Alternative 12
Error21.0
Cost968
\[\begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25 + c\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;y \cdot x + c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error35.8
Cost848
\[\begin{array}{l} t_1 := \left(-0.25 \cdot a\right) \cdot b\\ \mathbf{if}\;c \leq -7 \cdot 10^{+42}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-278}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;c \leq 900:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
Alternative 14
Error37.0
Cost456
\[\begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+40}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
Alternative 15
Error43.9
Cost64
\[c \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))