Average Error: 0.8 → 0.8
Time: 7.8s
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

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

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

  2. Final simplification0.8

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

Reproduce

herbie shell --seed 2019007 +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: 7.3s)Debug log

sample136.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

4.0ms
(/ (exp a) (+ (exp a) (exp b)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b
(/ (exp a) (+ (exp a) (exp b)))
0.0b
(+ (exp a) (exp b))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 52
Calls

2 calls. Slowest were:

7.0ms
(/ (exp a) (+ (exp a) (exp b)))
4.0ms
(+ (exp a) (exp b))

series435.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

377.0ms
(+ (exp a) (exp b))
57.0ms
(/ (exp a) (+ (exp a) (exp b)))

simplify602.0ms

Counts
44 → 58
Calls

44 calls. Slowest were:

250.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
80.0ms
(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
77.0ms
(- (+ (* 1/4 a) 1/2) (* 1/4 b))

prune490.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (exp a) (+ a (+ b 2)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 31
Calls

1 calls. Slowest were:

7.0ms
(/ (exp a) (+ a (+ b 2)))

series102.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

101.0ms
(/ (exp a) (+ a (+ b 2)))

simplify733.0ms

Counts
30 → 34
Calls

30 calls. Slowest were:

168.0ms
(+ (* a a) (- (* (+ b 2) (+ b 2)) (* a (+ b 2))))
152.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ a (+ b 2)) (+ a (+ b 2))) (+ a (+ b 2))))
43.0ms
(- (+ (* 1/4 a) 1/2) (* 1/4 b))

prune358.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune1.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.9b

regimes196.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals