Average Error: 0.6 → 0.6
Time: 9.3s
Precision: 64
Internal Precision: 128
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

    \[\leadsto \frac{e^{a}}{e^{a} + e^{b}}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1 (+ 1 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))

Details

Time bar (total: 8.9s)Debug log

sample102.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(/ (exp a) (+ (exp a) (exp b)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (exp a) (+ (exp a) (exp b)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
1 → 35
Calls

1 calls. Slowest were:

12.0ms
(/ (exp a) (+ (exp a) (exp b)))

series44.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

44.0ms
(/ (exp a) (+ (exp a) (exp b)))

simplify497.0ms

Counts
37 → 38
Calls

37 calls. Slowest were:

244.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
61.0ms
(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
36.0ms
(- (+ (* 1/4 a) 1/2) (* 1/4 b))

prune333.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
0.0b
(/ (exp a) (+ (exp a) (exp b)))
0.0b
(/ (exp a) (+ (exp a) (exp b)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
3 → 135
Calls

3 calls. Slowest were:

27.0ms
(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
13.0ms
(/ (exp a) (+ (exp a) (exp b)))
12.0ms
(/ (exp a) (+ (exp a) (exp b)))

series163.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

62.0ms
(/ (exp a) (+ (exp a) (exp b)))
61.0ms
(* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b)))))
40.0ms
(/ (exp a) (+ (exp a) (exp b)))

simplify2.0s

Counts
134 → 144
Calls

134 calls. Slowest were:

284.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
278.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
218.0ms
(* (* (* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b))))) (sqrt (/ (exp a) (+ (exp a) (exp b))))) (* (* (sqrt (/ (exp a) (+ (exp a) (exp b)))) (sqrt (/ (exp a) (+ (exp a) (exp b))))) (sqrt (/ (exp a) (+ (exp a) (exp b))))))

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample3.9s

Algorithm
intervals