Average Error: 0.1 → 0.1
Time: 29.0s
Precision: binary64
Cost: 26560
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
↓
\[\mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z + t\right) + a\right) + y \cdot i \]
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (fma (+ b -0.5) (log c) (+ (fma x (log y) (+ z t)) a)) (* y i)))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma((b + -0.5), log(c), (fma(x, log(y), (z + t)) + a)) + (y * i);
}

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end
↓
function code(x, y, z, t, a, b, c, i)
	return Float64(fma(Float64(b + -0.5), log(c), Float64(fma(x, log(y), Float64(z + t)) + a)) + Float64(y * i))
end

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z + t\right) + a\right) + y \cdot i

Error

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

  2. Applied egg-rr0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z + t\right) + a\right)} + y \cdot i \]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(b + -0.5, \log c, \mathsf{fma}\left(x, \log y, z + t\right) + a\right) + y \cdot i \]

Alternatives

Alternative 1
Error15.3
Cost34128
\[\begin{array}{l} t_1 := b \cdot \log c\\ t_2 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ t_3 := \log c \cdot \left(b + -0.5\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{+186}:\\ \;\;\;\;t + \left(z + t_1\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_1\\ \end{array} \]
Alternative 2
Error15.1
Cost34128
\[\begin{array}{l} t_1 := \log c \cdot \left(b + -0.5\right)\\ t_2 := t + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;t_1 \leq -50000000:\\ \;\;\;\;t + \left(t_1 + \left(z + a\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]
Alternative 3
Error3.4
Cost14408
\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;b + -0.5 \leq -2 \cdot 10^{+64}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;b + -0.5 \leq 10^{+109}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + t_1\right)\right)\right) + -0.5 \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(b \cdot \log c + \left(t_1 + \left(z + a\right)\right)\right)\\ \end{array} \]
Alternative 4
Error0.1
Cost14016
\[y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b + -0.5\right)\right) \]
Alternative 5
Error2.8
Cost13896
\[\begin{array}{l} t_1 := t + \left(b \cdot \log c + \left(x \cdot \log y + \left(z + a\right)\right)\right)\\ \mathbf{if}\;x \leq -5.422777038716161 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9765263626709002 \cdot 10^{+86}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error5.2
Cost13512
\[\begin{array}{l} \mathbf{if}\;x \leq -7.950853325577429 \cdot 10^{+154}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.1797500326286185 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(\log y, x, z + a\right)\\ \end{array} \]
Alternative 7
Error5.2
Cost7624
\[\begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -7.950853325577429 \cdot 10^{+154}:\\ \;\;\;\;t + \left(t_1 + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.1797500326286185 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b + -0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \left(z + t_1\right)\right)\\ \end{array} \]
Alternative 8
Error17.5
Cost7112
\[\begin{array}{l} t_1 := t + \left(z + b \cdot \log c\right)\\ \mathbf{if}\;b \leq -4.656817778038025 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.6251169723701468 \cdot 10^{+110}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error18.2
Cost7112
\[\begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -4.656817778038025 \cdot 10^{+182}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;b \leq 2.6251169723701468 \cdot 10^{+110}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + t_1\right)\\ \end{array} \]
Alternative 10
Error18.6
Cost6984
\[\begin{array}{l} t_1 := t + b \cdot \log c\\ \mathbf{if}\;b \leq -4.656817778038025 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.68618432308795 \cdot 10^{+209}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error21.2
Cost6852
\[\begin{array}{l} \mathbf{if}\;x \leq 1.71760390760121 \cdot 10^{+171}:\\ \;\;\;\;t + \left(a + \left(z + y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \log y\\ \end{array} \]
Alternative 12
Error39.3
Cost852
\[\begin{array}{l} \mathbf{if}\;a \leq 4.794507196349279 \cdot 10^{+25}:\\ \;\;\;\;z + t\\ \mathbf{elif}\;a \leq 1.4086239094905325 \cdot 10^{+79}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4.091303444971624 \cdot 10^{+137}:\\ \;\;\;\;z + t\\ \mathbf{elif}\;a \leq 3.929303643124749 \cdot 10^{+168}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;a \leq 1.8447724620291876 \cdot 10^{+192}:\\ \;\;\;\;z + t\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
Alternative 13
Error33.9
Cost848
\[\begin{array}{l} t_1 := t + \left(z + a\right)\\ \mathbf{if}\;z \leq -5.85043639249283 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.352921689122508 \cdot 10^{+98}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -5.237717282378348 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.964547879333636 \cdot 10^{-78}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error38.6
Cost588
\[\begin{array}{l} \mathbf{if}\;a \leq 4.091303444971624 \cdot 10^{+137}:\\ \;\;\;\;z + t\\ \mathbf{elif}\;a \leq 3.929303643124749 \cdot 10^{+168}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;a \leq 1.8447724620291876 \cdot 10^{+192}:\\ \;\;\;\;z + t\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
Alternative 15
Error24.0
Cost576
\[t + \left(a + \left(z + y \cdot i\right)\right) \]
Alternative 16
Error40.7
Cost452
\[\begin{array}{l} \mathbf{if}\;z \leq -2.3287553345203624 \cdot 10^{+163}:\\ \;\;\;\;t + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
Alternative 17
Error42.0
Cost192
\[z + t \]

Error

Reproduce

herbie shell --seed 2022306 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))