Average Error: 0.0 → 0.0
Time: 3.2s
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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 2.9s)Debug log

sample32.0ms

Algorithm
intervals

simplify49.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

49.0ms
(exp (- (- 1 (* x x))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 14
Calls

1 calls. Slowest were:

1.0ms
(exp (fma x x -1))

series17.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify169.0ms

Counts
8 → 17
Calls

8 calls. Slowest were:

121.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
31.0ms
(exp (* (cbrt (fma x x -1)) (cbrt (fma x x -1))))
7.0ms
(exp (sqrt (fma x x -1)))

prune114.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(expm1 (log1p (exp (fma x x -1))))
1.0b
(log1p (exp (fma x x -1)))
0.0b
(exp (fma x x -1))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
3 → 36
Calls

3 calls. Slowest were:

1.0ms
(exp (fma x x -1))
0.0ms
(log1p (exp (fma x x -1)))
0.0ms
(expm1 (log1p (exp (fma x x -1))))

series301.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

161.0ms
(expm1 (log1p (exp (fma x x -1))))
113.0ms
(log1p (exp (fma x x -1)))
26.0ms
(exp (fma x x -1))

simplify699.0ms

Counts
16 → 45
Calls

16 calls. Slowest were:

283.0ms
(- (+ (* 1/2 (/ (* (pow x 4) (exp -1)) (+ (exp -1) 1))) (+ (/ (* (pow x 2) (exp -1)) (+ (exp -1) 1)) (log (+ (exp -1) 1)))) (* 1/2 (/ (* (pow x 4) (pow (exp -1) 2)) (pow (+ (exp -1) 1) 2))))
182.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
117.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))

prune291.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

end0.0ms

sample1.1s

Algorithm
intervals