Average Error: 0.1 → 0.1
Time: 36.6s
Precision: binary64
Cost: 14016
\[ \begin{array}{c}[z, t, a] = \mathsf{sort}([z, t, a])\\ \end{array} \]
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
↓
\[\left(\left(\left(\left(z + x \cdot \log y\right) + t\right) + a\right) + \left(b + -0.5\right) \cdot \log c\right) + y \cdot i \]
(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
 (+ (+ (+ (+ (+ z (* x (log y))) 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 (((((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 ((((z + (x * log(y))) + t) + a) + ((b + -0.5) * log(c))) + (y * i);
}

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function
↓
real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((z + (x * log(y))) + t) + a) + ((b + (-0.5d0)) * log(c))) + (y * i)
end function

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}
↓
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((z + (x * Math.log(y))) + t) + a) + ((b + -0.5) * Math.log(c))) + (y * i);
}

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
↓
def code(x, y, z, t, a, b, c, i):
	return ((((z + (x * math.log(y))) + t) + a) + ((b + -0.5) * math.log(c))) + (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(Float64(Float64(Float64(Float64(z + Float64(x * log(y))) + t) + a) + Float64(Float64(b + -0.5) * log(c))) + Float64(y * i))
end

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end
↓
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((z + (x * log(y))) + t) + a) + ((b + -0.5) * log(c))) + (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[(N[(N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $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
↓
\left(\left(\left(\left(z + x \cdot \log y\right) + t\right) + a\right) + \left(b + -0.5\right) \cdot \log c\right) + y \cdot i

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.1

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

Alternatives

Alternative 1
Error2.8
Cost14024
\[\begin{array}{l} t_1 := \left(b + -0.5\right) \cdot \log c\\ t_2 := x \cdot \log y + \left(a + \left(t_1 + \left(z + t\right)\right)\right)\\ \mathbf{if}\;x \leq -5.716316854976589 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2231302730139545 \cdot 10^{+172}:\\ \;\;\;\;y \cdot i + \left(t_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error1.3
Cost13888
\[y \cdot i + \left(\left(\left(\left(z + x \cdot \log y\right) + t\right) + a\right) + b \cdot \log c\right) \]
Alternative 3
Error31.2
Cost8692
\[\begin{array}{l} t_1 := a + y \cdot i\\ t_2 := t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\\ t_3 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.7967934221268535 \cdot 10^{+170}:\\ \;\;\;\;t + t_3\\ \mathbf{elif}\;x \leq -3.3648615596759266 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.277188643616921 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.447591149030271 \cdot 10^{+38}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;x \leq -3598.5314089872063:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.144372801047995 \cdot 10^{-69}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;x \leq -6.502266282918013 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.022548552918159 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.540896415146927 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.1051301033771175 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.237179683163301 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.5123255847114922 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.643974590550625 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_3\\ \end{array} \]
Alternative 4
Error30.6
Cost8692
\[\begin{array}{l} t_1 := z + y \cdot i\\ t_2 := a + y \cdot i\\ t_3 := x \cdot \log y\\ t_4 := \left(b + -0.5\right) \cdot \log c\\ t_5 := t + \left(a + t_4\right)\\ t_6 := t + \left(z + t_4\right)\\ \mathbf{if}\;x \leq -3.7967934221268535 \cdot 10^{+170}:\\ \;\;\;\;t + t_3\\ \mathbf{elif}\;x \leq -3598.5314089872063:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -6.144372801047995 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.502266282918013 \cdot 10^{-111}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -5.022548552918159 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.540896415146927 \cdot 10^{-203}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -4.1051301033771175 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2521713706396535 \cdot 10^{-269}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 1.5123255847114922 \cdot 10^{-81}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.8225637548510077 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.47874495203515 \cdot 10^{+127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 8.839024006959736 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.992024344112489 \cdot 10^{+191}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_3\\ \end{array} \]
Alternative 5
Error34.0
Cost8036
\[\begin{array}{l} t_1 := a + y \cdot i\\ t_2 := x \cdot \log y\\ t_3 := z + y \cdot i\\ \mathbf{if}\;x \leq -3.7967934221268535 \cdot 10^{+170}:\\ \;\;\;\;t + t_2\\ \mathbf{elif}\;x \leq -14638954680.566841:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;x \leq -8.650026262261639 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.487618239874833 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.2521713706396535 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.5123255847114922 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.222479102565921 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.47874495203515 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.643974590550625 \cdot 10^{+185}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_2\\ \end{array} \]
Alternative 6
Error34.3
Cost7908
\[\begin{array}{l} t_1 := a + y \cdot i\\ t_2 := t + x \cdot \log y\\ t_3 := z + y \cdot i\\ \mathbf{if}\;x \leq -3.7967934221268535 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -14638954680.566841:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;x \leq -8.650026262261639 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.487618239874833 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.2521713706396535 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.5123255847114922 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.222479102565921 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5.47874495203515 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.643974590550625 \cdot 10^{+185}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error33.7
Cost7776
\[\begin{array}{l} t_1 := z + y \cdot i\\ t_2 := a + y \cdot i\\ t_3 := t + x \cdot \log y\\ \mathbf{if}\;x \leq -5.784464498074216 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.650026262261639 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.487618239874833 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2521713706396535 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5123255847114922 \cdot 10^{-81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.222479102565921 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.47874495203515 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.643974590550625 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 8
Error7.4
Cost7752
\[\begin{array}{l} t_1 := t + \left(a + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{if}\;b + -0.5 \leq -5 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b + -0.5 \leq 10^{+183}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error7.8
Cost7624
\[\begin{array}{l} t_1 := t + \left(a + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{if}\;b + -0.5 \leq -5 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b + -0.5 \leq 10^{+183}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error3.8
Cost7624
\[\begin{array}{l} t_1 := y \cdot i + \left(x \cdot \log y + \left(z + a\right)\right)\\ \mathbf{if}\;x \leq -3.7967934221268535 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.518136136435103 \cdot 10^{+176}:\\ \;\;\;\;y \cdot i + \left(\left(b + -0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error29.2
Cost6988
\[\begin{array}{l} t_1 := a + y \cdot i\\ \mathbf{if}\;z \leq -2.090277516213654 \cdot 10^{+159}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -1.2527230682529209 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -513836923887.5104:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error37.4
Cost852
\[\begin{array}{l} \mathbf{if}\;z \leq -2.090277516213654 \cdot 10^{+159}:\\ \;\;\;\;z + t\\ \mathbf{elif}\;z \leq -3.685431990729037 \cdot 10^{+35}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.2194527139265869 \cdot 10^{-8}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -1.1327074885104188 \cdot 10^{-133}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -6.947741134214382 \cdot 10^{-203}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 13
Error37.2
Cost852
\[\begin{array}{l} \mathbf{if}\;z \leq -2.090277516213654 \cdot 10^{+159}:\\ \;\;\;\;z + t\\ \mathbf{elif}\;z \leq -3.685431990729037 \cdot 10^{+35}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -1.2194527139265869 \cdot 10^{-8}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;z \leq -1.1327074885104188 \cdot 10^{-133}:\\ \;\;\;\;t + a\\ \mathbf{elif}\;z \leq -6.947741134214382 \cdot 10^{-203}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
Alternative 14
Error29.9
Cost452
\[\begin{array}{l} \mathbf{if}\;a \leq 3.279624851990403 \cdot 10^{+123}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + a\\ \end{array} \]
Alternative 15
Error28.7
Cost452
\[\begin{array}{l} \mathbf{if}\;z \leq -2.090277516213654 \cdot 10^{+159}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
Alternative 16
Error42.7
Cost324
\[\begin{array}{l} \mathbf{if}\;a \leq 2.71622350357042 \cdot 10^{+119}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
Alternative 17
Error46.5
Cost64
\[a \]

Error

Reproduce

herbie shell --seed 2022294 
(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)))