?

Average Error: 15.28% → 0.14%
Time: 14.0s
Precision: binary64
Cost: 960

?

\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
↓
\[\frac{x}{y} + \left(-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\right) \]
(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (+ -2.0 (* (/ 1.0 t) (+ 2.0 (/ 2.0 z))))))
double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}
↓
double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / z))));
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function
↓
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((-2.0d0) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z))))
end function

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}
↓
public static double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / z))));
}

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
↓
def code(x, y, z, t):
	return (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / z))))

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end
↓
function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(-2.0 + Float64(Float64(1.0 / t) * Float64(2.0 + Float64(2.0 / z)))))
end

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end
↓
function tmp = code(x, y, z, t)
	tmp = (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / z))));
end

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(1.0 / t), $MachinePrecision] * N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(-2 + \frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.28%
Target0.11%
Herbie0.14%
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \]

Derivation?

  1. Initial program 15.28

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

  2. Simplified0.11

    \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2 + \frac{2}{z}}{t}\right)} \]
    Proof

    [Start]15.28

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

    +-rgt-identity [<=]15.28

    \[ \color{blue}{\left(\frac{x}{y} + 0\right)} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

    mul0-lft [<=]15.28

    \[ \left(\frac{x}{y} + \color{blue}{0 \cdot \frac{2}{t \cdot z}}\right) + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

    associate-+r+ [<=]15.28

    \[ \color{blue}{\frac{x}{y} + \left(0 \cdot \frac{2}{t \cdot z} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)} \]

    mul0-lft [=>]15.28

    \[ \frac{x}{y} + \left(\color{blue}{0} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right) \]

    +-lft-identity [=>]15.28

    \[ \frac{x}{y} + \color{blue}{\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}} \]

    sub-neg [=>]15.28

    \[ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \color{blue}{\left(1 + \left(-t\right)\right)}}{t \cdot z} \]

    distribute-rgt-in [=>]15.28

    \[ \frac{x}{y} + \frac{2 + \color{blue}{\left(1 \cdot \left(z \cdot 2\right) + \left(-t\right) \cdot \left(z \cdot 2\right)\right)}}{t \cdot z} \]

    associate-+r+ [=>]15.28

    \[ \frac{x}{y} + \frac{\color{blue}{\left(2 + 1 \cdot \left(z \cdot 2\right)\right) + \left(-t\right) \cdot \left(z \cdot 2\right)}}{t \cdot z} \]

    cancel-sign-sub-inv [<=]15.28

    \[ \frac{x}{y} + \frac{\color{blue}{\left(2 + 1 \cdot \left(z \cdot 2\right)\right) - t \cdot \left(z \cdot 2\right)}}{t \cdot z} \]

    div-sub [=>]15.27

    \[ \frac{x}{y} + \color{blue}{\left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} - \frac{t \cdot \left(z \cdot 2\right)}{t \cdot z}\right)} \]

    associate-*r* [=>]15.27

    \[ \frac{x}{y} + \left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} - \frac{\color{blue}{\left(t \cdot z\right) \cdot 2}}{t \cdot z}\right) \]

    associate-*l/ [<=]15.19

    \[ \frac{x}{y} + \left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} - \color{blue}{\frac{t \cdot z}{t \cdot z} \cdot 2}\right) \]

    *-inverses [=>]0.26

    \[ \frac{x}{y} + \left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} - \color{blue}{1} \cdot 2\right) \]

    metadata-eval [=>]0.26

    \[ \frac{x}{y} + \left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} - \color{blue}{2}\right) \]

    sub-neg [=>]0.26

    \[ \frac{x}{y} + \color{blue}{\left(\frac{2 + 1 \cdot \left(z \cdot 2\right)}{t \cdot z} + \left(-2\right)\right)} \]

  3. Applied egg-rr0.14

    \[\leadsto \frac{x}{y} + \left(-2 + \color{blue}{\frac{1}{t} \cdot \left(2 + \frac{2}{z}\right)}\right) \]

  4. Final simplification0.14

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

Alternatives

Alternative 1
Error25.33%
Cost1748
\[\begin{array}{l} t_1 := -2 + \frac{2}{t \cdot z}\\ t_2 := -2 + \frac{2}{t}\\ t_3 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-312}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.5 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2.75 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 2
Error30.8%
Cost1620
\[\begin{array}{l} t_1 := -2 + \frac{2}{t}\\ t_2 := \frac{x}{y} + -2\\ t_3 := -2 + \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-312}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;\frac{x}{y} \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error38.55%
Cost1376
\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ t_3 := \frac{2}{t \cdot z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-235}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error38.51%
Cost1376
\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-236}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 5
Error7.56%
Cost1097
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
Alternative 6
Error7.55%
Cost1097
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
Alternative 7
Error7.36%
Cost1096
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 200000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
Alternative 8
Error53.29%
Cost984
\[\begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+166}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+199}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
Alternative 9
Error21.42%
Cost976
\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2500000000000:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error1.27%
Cost969
\[\begin{array}{l} \mathbf{if}\;z \leq -19000000000 \lor \neg \left(z \leq 0.042\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \end{array} \]
Alternative 11
Error1.27%
Cost969
\[\begin{array}{l} \mathbf{if}\;z \leq -19000000000 \lor \neg \left(z \leq 0.042\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{t}}{z}\right)\\ \end{array} \]
Alternative 12
Error30.35%
Cost840
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -12600000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.4 \cdot 10^{+14}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
Alternative 13
Error0.11%
Cost832
\[\frac{x}{y} + \left(-2 + \frac{2 + \frac{2}{z}}{t}\right) \]
Alternative 14
Error30.65%
Cost585
\[\begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-69} \lor \neg \left(t \leq 9.4 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
Alternative 15
Error53.64%
Cost456
\[\begin{array}{l} \mathbf{if}\;t \leq -195:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
Alternative 16
Error74.61%
Cost64
\[-2 \]

Error

Reproduce?

herbie shell --seed 2023121 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))