Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{(x \cdot x + -1)_*}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Initial simplification0.0

    \[\leadsto e^{(x \cdot x + -1)_*}\]

  3. Final simplification0.0

    \[\leadsto e^{(x \cdot x + -1)_*}\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 859.0ms)Debug log

start44.0ms

Algorithm
intervals

setup80.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(exp (fma x x -1))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 14
Calls

1 calls. Slowest were:

3.0ms
(exp (fma x x -1))

series17.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

17.0ms
(exp (fma x x -1))

simplify123.0ms

Counts
8 → 17
Calls

8 calls. Slowest were:

82.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
29.0ms
(exp (* (cbrt (fma x x -1)) (cbrt (fma x x -1))))
4.0ms
(exp (sqrt (fma x x -1)))

prune175.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(pow E (fma x x -1))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 14
Calls

1 calls. Slowest were:

1.0ms
(pow E (fma x x -1))

series39.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

39.0ms
(pow E (fma x x -1))

simplify135.0ms

Counts
7 → 17
Calls

7 calls. Slowest were:

115.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
5.0ms
(exp (fma x x -1))
4.0ms
(exp (fma x x -1))

prune184.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms