?

Average Error: 0.0 → 0.0
Time: 14.7s
Precision: binary64
Cost: 13632

?

\[\left(\left(\left(\left(0 \leq va \land va \leq 10000000\right) \land \left(0 \leq vb \land vb \leq 10000000\right)\right) \land \left(0 \leq p \land p \leq 1\right)\right) \land \left(1 \leq na \land na \leq 10000000\right)\right) \land \left(1 \leq nb \land nb \leq 10000000\right)\]
\[\frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right| \]
↓
\[\frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right| \]
(FPCore (va vb p na nb)
 :precision binary64
 (- (/ (* (fabs (- va vb)) (- 1.0 p)) p) (fabs (- na nb))))
↓
(FPCore (va vb p na nb)
 :precision binary64
 (- (/ (* (fabs (- va vb)) (- 1.0 p)) p) (fabs (- na nb))))
double code(double va, double vb, double p, double na, double nb) {
	return ((fabs((va - vb)) * (1.0 - p)) / p) - fabs((na - nb));
}
↓
double code(double va, double vb, double p, double na, double nb) {
	return ((fabs((va - vb)) * (1.0 - p)) / p) - fabs((na - nb));
}

real(8) function code(va, vb, p, na, nb)
    real(8), intent (in) :: va
    real(8), intent (in) :: vb
    real(8), intent (in) :: p
    real(8), intent (in) :: na
    real(8), intent (in) :: nb
    code = ((abs((va - vb)) * (1.0d0 - p)) / p) - abs((na - nb))
end function
↓
real(8) function code(va, vb, p, na, nb)
    real(8), intent (in) :: va
    real(8), intent (in) :: vb
    real(8), intent (in) :: p
    real(8), intent (in) :: na
    real(8), intent (in) :: nb
    code = ((abs((va - vb)) * (1.0d0 - p)) / p) - abs((na - nb))
end function

public static double code(double va, double vb, double p, double na, double nb) {
	return ((Math.abs((va - vb)) * (1.0 - p)) / p) - Math.abs((na - nb));
}
↓
public static double code(double va, double vb, double p, double na, double nb) {
	return ((Math.abs((va - vb)) * (1.0 - p)) / p) - Math.abs((na - nb));
}

def code(va, vb, p, na, nb):
	return ((math.fabs((va - vb)) * (1.0 - p)) / p) - math.fabs((na - nb))
↓
def code(va, vb, p, na, nb):
	return ((math.fabs((va - vb)) * (1.0 - p)) / p) - math.fabs((na - nb))

function code(va, vb, p, na, nb)
	return Float64(Float64(Float64(abs(Float64(va - vb)) * Float64(1.0 - p)) / p) - abs(Float64(na - nb)))
end
↓
function code(va, vb, p, na, nb)
	return Float64(Float64(Float64(abs(Float64(va - vb)) * Float64(1.0 - p)) / p) - abs(Float64(na - nb)))
end

function tmp = code(va, vb, p, na, nb)
	tmp = ((abs((va - vb)) * (1.0 - p)) / p) - abs((na - nb));
end
↓
function tmp = code(va, vb, p, na, nb)
	tmp = ((abs((va - vb)) * (1.0 - p)) / p) - abs((na - nb));
end

code[va_, vb_, p_, na_, nb_] := N[(N[(N[(N[Abs[N[(va - vb), $MachinePrecision]], $MachinePrecision] * N[(1.0 - p), $MachinePrecision]), $MachinePrecision] / p), $MachinePrecision] - N[Abs[N[(na - nb), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[va_, vb_, p_, na_, nb_] := N[(N[(N[(N[Abs[N[(va - vb), $MachinePrecision]], $MachinePrecision] * N[(1.0 - p), $MachinePrecision]), $MachinePrecision] / p), $MachinePrecision] - N[Abs[N[(na - nb), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right|
↓
\frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right|

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[\frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right| \]

  2. Final simplification0.0

    \[\leadsto \frac{\left|va - vb\right| \cdot \left(1 - p\right)}{p} - \left|na - nb\right| \]

Alternatives

Alternative 1
Error0.2
Cost13632
\[\left|va - vb\right| \cdot \frac{1 - p}{p} - \left|na - nb\right| \]
Alternative 2
Error21.3
Cost6976
\[\frac{vb - va}{p} - \left|na - nb\right| \]
Alternative 3
Error35.6
Cost708
\[\begin{array}{l} \mathbf{if}\;p \leq 2.25 \cdot 10^{-122}:\\ \;\;\;\;nb + \left(\frac{vb - va}{p} - na\right)\\ \mathbf{else}:\\ \;\;\;\;na + \left(\left(vb - va\right) - nb\right)\\ \end{array} \]
Alternative 4
Error43.8
Cost580
\[\begin{array}{l} \mathbf{if}\;p \leq 9.2 \cdot 10^{-132}:\\ \;\;\;\;va \cdot \left(\frac{1}{p} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;-na\\ \end{array} \]
Alternative 5
Error51.5
Cost448
\[na + \left(\left(vb - va\right) - nb\right) \]
Alternative 6
Error58.7
Cost128
\[-na \]
Alternative 7
Error61.1
Cost64
\[nb \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (va vb p na nb)
  :name "abs(va-vb)*(1-p)/p-abs(na-nb)"
  :precision binary64
  :pre (and (and (and (and (and (<= 0.0 va) (<= va 10000000.0)) (and (<= 0.0 vb) (<= vb 10000000.0))) (and (<= 0.0 p) (<= p 1.0))) (and (<= 1.0 na) (<= na 10000000.0))) (and (<= 1.0 nb) (<= nb 10000000.0)))
  (- (/ (* (fabs (- va vb)) (- 1.0 p)) p) (fabs (- na nb))))