Exp of sum of logs

Average Error: 5.7 → 0

Time: 1.7s

Precision: binary64

Cost: 192

Math

\[e^{\log a + \log b} \]

↓

\[a \cdot b \]

FPCore

(FPCore (a b) :precision binary64 (exp (+ (log a) (log b))))

↓

(FPCore (a b) :precision binary64 (* a b))

C

double code(double a, double b) {
	return exp((log(a) + log(b)));
}

↓

double code(double a, double b) {
	return a * b;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp((log(a) + log(b)))
end function

↓

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a * b
end function

Java

public static double code(double a, double b) {
	return Math.exp((Math.log(a) + Math.log(b)));
}

↓

public static double code(double a, double b) {
	return a * b;
}

Python

def code(a, b):
	return math.exp((math.log(a) + math.log(b)))

↓

def code(a, b):
	return a * b

Julia

function code(a, b)
	return exp(Float64(log(a) + log(b)))
end

↓

function code(a, b)
	return Float64(a * b)
end

MATLAB

function tmp = code(a, b)
	tmp = exp((log(a) + log(b)));
end

↓

function tmp = code(a, b)
	tmp = a * b;
end

Wolfram

code[a_, b_] := N[Exp[N[(N[Log[a], $MachinePrecision] + N[Log[b], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

↓

code[a_, b_] := N[(a * b), $MachinePrecision]

Target

Original	5.7
Target	0
Herbie	0

\[a \cdot b \]

Derivation

1. Initial program 5.7

   \[e^{\log a + \log b} \]

2. Simplified 0

   \[\leadsto \color{blue}{a \cdot b} \]
   Proof

   [Start] 5.7	\[ e^{\log a + \log b} \]
   exp-sum [=>] 5.4	\[ \color{blue}{e^{\log a} \cdot e^{\log b}} \]
   rem-exp-log [=>] 4.7	\[ \color{blue}{a} \cdot e^{\log b} \]
   rem-exp-log [=>] 0	\[ a \cdot \color{blue}{b} \]

3. Final simplification 0

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023046 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

  (exp (+ (log a) (log b))))