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

↓

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

(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 (/ (+ 2.0 (/ 2.0 z)) t))))

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 + ((2.0 + (2.0 / z)) / t));
}

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) + ((2.0d0 + (2.0d0 / z)) / t))
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 + ((2.0 + (2.0 / z)) / t));
}

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 + ((2.0 + (2.0 / z)) / t))

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(2.0 + Float64(2.0 / z)) / t)))
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 + ((2.0 + (2.0 / z)) / t));
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[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $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{2 + \frac{2}{z}}{t}\right)

Original	9.1
Target	0.1
Herbie	0.1

Derivation

Initial program 9.1
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
Simplified0.1
\[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2 + \frac{2}{z}}{t}\right)} \]
Proof
(+.f64 (/.f64 x y) (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (Rewrite<= metadata-eval (*.f64 2 -1)) (/.f64 (+.f64 2 (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (Rewrite<= metadata-eval (/.f64 2 1)) (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (/.f64 2 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 2 z) z)) (/.f64 2 z)) t))): 21 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 2)) z) (/.f64 2 z)) t))): 12 points increase in error, 21 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (/.f64 (*.f64 z 2) (Rewrite<= *-lft-identity_binary64 (*.f64 1 z))) (/.f64 2 z)) t))): 0 points increase in error, 12 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 z 1) (/.f64 2 z))) (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (*.f64 (Rewrite=> /-rgt-identity_binary64 z) (/.f64 2 z)) (/.f64 2 z)) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (*.f64 z (/.f64 2 z)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 2 z)))) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (/.f64 2 z) (+.f64 z 1))) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (*.f64 (/.f64 2 z) (+.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 z)) 1)) t))): 23 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 2 z) (/.f64 (+.f64 (*.f64 1 z) 1) t))))): 0 points increase in error, 23 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 (+.f64 (*.f64 1 z) 1) t) (/.f64 2 z))))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (+.f64 (*.f64 1 z) 1) 2) (*.f64 t z))))): 2 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (Rewrite<= distribute-rgt1-in_binary64 (+.f64 2 (*.f64 (*.f64 1 z) 2))) (*.f64 t z)))): 12 points increase in error, 2 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 2 (Rewrite<= associate-*r*_binary64 (*.f64 1 (*.f64 z 2)))) (*.f64 t z)))): 21 points increase in error, 14 points decrease in error
(+.f64 (/.f64 x y) (Rewrite=> +-commutative_binary64 (+.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (*.f64 2 -1)))): 0 points increase in error, 21 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (Rewrite=> metadata-eval -2))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (Rewrite<= metadata-eval (neg.f64 2)))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) 2))): 23 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (Rewrite<= metadata-eval (*.f64 1 2)))): 0 points increase in error, 23 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (*.f64 (Rewrite<= *-inverses_binary64 (/.f64 (*.f64 t z) (*.f64 t z))) 2))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (*.f64 t z) 2) (*.f64 t z))))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t z)) (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z 2))) (*.f64 t z)))): 13 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 t (*.f64 z 2))) (*.f64 t z)))): 0 points increase in error, 13 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (+.f64 2 (*.f64 1 (*.f64 z 2))) (*.f64 (neg.f64 t) (*.f64 z 2)))) (*.f64 t z))): 2 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 2 (+.f64 (*.f64 1 (*.f64 z 2)) (*.f64 (neg.f64 t) (*.f64 z 2))))) (*.f64 t z))): 13 points increase in error, 2 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (*.f64 z 2) (+.f64 1 (neg.f64 t))))) (*.f64 t z))): 0 points increase in error, 13 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (Rewrite<= sub-neg_binary64 (-.f64 1 t)))) (*.f64 t z))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (Rewrite<= +-lft-identity_binary64 (+.f64 0 (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z))))): 13 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (Rewrite<= mul0-lft_binary64 (*.f64 0 (/.f64 2 (*.f64 t z)))) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z)))): 0 points increase in error, 1 points decrease in error
(Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 (/.f64 x y) (*.f64 0 (/.f64 2 (*.f64 t z)))) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z)))): 2 points increase in error, 12 points decrease in error
(+.f64 (+.f64 (/.f64 x y) (Rewrite=> mul0-lft_binary64 0)) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z))): 0 points increase in error, 2 points decrease in error
(+.f64 (Rewrite=> +-rgt-identity_binary64 (/.f64 x y)) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z))): 0 points increase in error, 0 points decrease in error
Final simplification0.1
\[\leadsto \frac{x}{y} + \left(-2 + \frac{2 + \frac{2}{z}}{t}\right) \]

Alternatives

Alternative 1
Error	27.4
Cost	1377

\[\begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+139} \lor \neg \left(z \leq 8.8 \cdot 10^{+269}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 2
Error	27.5
Cost	1377

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := \frac{2}{z \cdot t}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+139} \lor \neg \left(z \leq 1.6 \cdot 10^{+267}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 3
Error	18.1
Cost	1372

\[\begin{array}{l} t_1 := \frac{\frac{2}{t}}{z}\\ t_2 := \frac{x}{y} + \frac{2}{t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-206}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	13.1
Cost	1369

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-179} \lor \neg \left(z \leq 1.1 \cdot 10^{-126}\right) \land z \leq 3.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	30.7
Cost	1232

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.2 \cdot 10^{-154}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 8.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 12200:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6
Error	5.4
Cost	1225

\[\begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -35 \lor \neg \left(\frac{x}{y} \leq 2.2 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y} + t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \left(-2 + t_1\right)\\ \end{array} \]

Alternative 7
Error	6.3
Cost	1106

\[\begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-14} \lor \neg \left(z \leq -9 \cdot 10^{-75}\right) \land \left(z \leq -1.35 \cdot 10^{-112} \lor \neg \left(z \leq 5.4 \cdot 10^{-9}\right)\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 8
Error	19.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -35:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9
Error	19.7
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.68:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.4 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10
Error	12.8
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+44} \lor \neg \left(t \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 11
Error	33.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 12
Error	47.7
Cost	64

\[-2 \]

Error

Try it out

Target

Derivation

Alternatives

Error

Reproduce

In
Out