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

↓

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

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

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 (((2.0 + (2.0 / z)) / t) + (x / y)) + -2.0;
}

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 = (((2.0d0 + (2.0d0 / z)) / t) + (x / y)) + (-2.0d0)
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 (((2.0 + (2.0 / z)) / t) + (x / y)) + -2.0;
}

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

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(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + Float64(x / y)) + -2.0)
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 = (((2.0 + (2.0 / z)) / t) + (x / y)) + -2.0;
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[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]

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

↓

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

Original	9.5
Target	0.1
Herbie	0.1

Derivation

Initial program 9.5
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
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))): 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))): 6 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (+.f64 (*.f64 (/.f64 2 z) z) (Rewrite<= *-rgt-identity_binary64 (*.f64 (/.f64 2 z) 1))) t))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 (/.f64 2 z) (+.f64 z 1))) t))): 0 points increase in error, 1 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 2 z) (/.f64 (+.f64 z 1) t))))): 49 points increase in error, 9 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 (+.f64 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 z 1) 2) (*.f64 t z))))): 17 points increase in error, 52 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (*.f64 2 -1) (/.f64 (Rewrite<= distribute-rgt1-in_binary64 (+.f64 2 (*.f64 z 2))) (*.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (Rewrite=> +-commutative_binary64 (+.f64 (/.f64 (+.f64 2 (*.f64 z 2)) (*.f64 t z)) (*.f64 2 -1)))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (+.f64 (/.f64 (+.f64 2 (*.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 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 z 2)) (*.f64 t z)) 2))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 z 2)) (*.f64 t z)) (Rewrite<= metadata-eval (*.f64 1 2)))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.f64 z 2)) (*.f64 t z)) (*.f64 (Rewrite<= *-inverses_binary64 (/.f64 (*.f64 t z) (*.f64 t z))) 2))): 42 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (-.f64 (/.f64 (+.f64 2 (*.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 z 2)) (*.f64 t z)) (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z 2))) (*.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 2 (*.f64 z 2)) (*.f64 t (*.f64 z 2))) (*.f64 t z)))): 1 points increase in error, 1 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (+.f64 2 (*.f64 z 2)) (*.f64 (neg.f64 t) (*.f64 z 2)))) (*.f64 t z))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 2 (+.f64 (*.f64 z 2) (*.f64 (neg.f64 t) (*.f64 z 2))))) (*.f64 t z))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (+.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (*.f64 z 2))) (*.f64 (neg.f64 t) (*.f64 z 2)))) (*.f64 t z))): 0 points increase in error, 0 points decrease in error
(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (Rewrite=> distribute-rgt-out_binary64 (*.f64 (*.f64 z 2) (+.f64 1 (neg.f64 t))))) (*.f64 t z))): 0 points increase in error, 0 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
Applied egg-rr40.1
\[\leadsto \color{blue}{{\left(\sqrt{\frac{2 + \frac{2}{z}}{t} + \left(\frac{x}{y} + -2\right)}\right)}^{2}} \]
Applied egg-rr0.1
\[\leadsto \color{blue}{\left(\frac{2 + \frac{2}{z}}{t} + \frac{x}{y}\right) + -2} \]
Final simplification0.1
\[\leadsto \left(\frac{2 + \frac{2}{z}}{t} + \frac{x}{y}\right) + -2 \]

Alternatives

Alternative 1
Error	30.9
Cost	1492

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.946867349422963 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -8.99783550035811 \cdot 10^{-22}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5800303978682455 \cdot 10^{-251}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq -3.7347508532885096 \cdot 10^{-287}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.2671773162465691 \cdot 10^{-12}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 2
Error	36.4
Cost	1248

\[\begin{array}{l} \mathbf{if}\;z \leq -1.454384721477553 \cdot 10^{+52}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -1.6639327317596764 \cdot 10^{-18}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.1740982003682353 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 8.019827125614732 \cdot 10^{+110}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 7.87100454991202 \cdot 10^{+167}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq 5.801229469311435 \cdot 10^{+214}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 7.417628586407048 \cdot 10^{+233}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq 1.4487303697931005 \cdot 10^{+262}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3
Error	24.1
Cost	1244

\[\begin{array}{l} t_1 := \frac{\frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + -2\\ t_3 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.6639327317596764 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.678344889848503 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2743215.8959457707:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.417628586407048 \cdot 10^{+233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.559874672623735 \cdot 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	19.5
Cost	980

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -82257379.25517705:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1030134342379839 \cdot 10^{-54}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 2743215.8959457707:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.417628586407048 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.559874672623735 \cdot 10^{+267}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	12.4
Cost	972

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.482555928041924 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.712647934652672 \cdot 10^{-9}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.0137701661321138 \cdot 10^{-13}:\\ \;\;\;\;\frac{2}{t} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	0.8
Cost	968

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -82257379.25517705:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8029057112155793 \cdot 10^{-10}:\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	0.8
Cost	968

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -82257379.25517705:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8029057112155793 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	12.4
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.482555928041924 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.712647934652672 \cdot 10^{-9}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.0137701661321138 \cdot 10^{-13}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.946867349422963 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.512209864605213 \cdot 10^{+20}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10
Error	8.1
Cost	840

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -6.989627318054879 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1030134342379839 \cdot 10^{-54}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	6.5
Cost	840

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -1.6639327317596764 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1030134342379839 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	33.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -2.712647934652672 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 58.68371480530138:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 13
Error	47.3
Cost	64

\[-2 \]

Error

Try it out

Target

Derivation

Alternatives

Error

Reproduce

In
Out