?

Average Error: 0.4 → 0.2
Time: 1.8min
Precision: binary64
Cost: 576

?

\[\left(\left(\left(\left(\left(\left(\left(\left(1 \leq a \land a \leq 2\right) \land 2 \leq b\right) \land b \leq 4\right) \land 4 \leq c\right) \land c \leq 8\right) \land 8 \leq d\right) \land d \leq 16\right) \land 16 \leq e\right) \land e \leq 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a \]
↓
\[d + \left(e + \left(\left(c + b\right) + a\right)\right) \]
(FPCore (a b c d e) :precision binary64 (+ (+ (+ (+ e d) c) b) a))
↓
(FPCore (a b c d e) :precision binary64 (+ d (+ e (+ (+ c b) a))))
double code(double a, double b, double c, double d, double e) {
	return (((e + d) + c) + b) + a;
}
↓
double code(double a, double b, double c, double d, double e) {
	return d + (e + ((c + b) + a));
}

real(8) function code(a, b, c, d, e)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8), intent (in) :: e
    code = (((e + d) + c) + b) + a
end function
↓
real(8) function code(a, b, c, d, e)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8), intent (in) :: e
    code = d + (e + ((c + b) + a))
end function

public static double code(double a, double b, double c, double d, double e) {
	return (((e + d) + c) + b) + a;
}
↓
public static double code(double a, double b, double c, double d, double e) {
	return d + (e + ((c + b) + a));
}

def code(a, b, c, d, e):
	return (((e + d) + c) + b) + a
↓
def code(a, b, c, d, e):
	return d + (e + ((c + b) + a))

function code(a, b, c, d, e)
	return Float64(Float64(Float64(Float64(e + d) + c) + b) + a)
end
↓
function code(a, b, c, d, e)
	return Float64(d + Float64(e + Float64(Float64(c + b) + a)))
end

function tmp = code(a, b, c, d, e)
	tmp = (((e + d) + c) + b) + a;
end
↓
function tmp = code(a, b, c, d, e)
	tmp = d + (e + ((c + b) + a));
end

code[a_, b_, c_, d_, e_] := N[(N[(N[(N[(e + d), $MachinePrecision] + c), $MachinePrecision] + b), $MachinePrecision] + a), $MachinePrecision]
↓
code[a_, b_, c_, d_, e_] := N[(d + N[(e + N[(N[(c + b), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
d + \left(e + \left(\left(c + b\right) + a\right)\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e \]

Derivation?

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a \]

  2. Applied egg-rr0.2

    \[\leadsto \color{blue}{d + \left(e + \left(\left(c + b\right) + a\right)\right)} \]

Alternatives

Alternative 1
Error0.3
Cost576
\[c + \left(\left(a + d\right) + \left(b + e\right)\right) \]
Alternative 2
Error47.6
Cost448
\[c + \left(d + \left(b + e\right)\right) \]
Alternative 3
Error47.6
Cost448
\[c + \left(\left(e + d\right) + b\right) \]
Alternative 4
Error47.6
Cost448
\[\left(c + \left(e + d\right)\right) + b \]
Alternative 5
Error49.2
Cost320
\[c + \left(e + d\right) \]
Alternative 6
Error50.5
Cost192
\[d + e \]
Alternative 7
Error51.9
Cost64
\[e \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (and (and (and (and (and (and (and (and (and (<= 1.0 a) (<= a 2.0)) (<= 2.0 b)) (<= b 4.0)) (<= 4.0 c)) (<= c 8.0)) (<= 8.0 d)) (<= d 16.0)) (<= 16.0 e)) (<= e 32.0))

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))