Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{\frac{e}{{\left(e^{x}\right)}^{x}}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{e^{x \cdot x}}{e}}\]
  3. Using strategy rm

  4. Applied exp-prod0.0

    \[\leadsto \frac{\color{blue}{{\left(e^{x}\right)}^{x}}}{e}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.0

    \[\leadsto \frac{\color{blue}{1 \cdot {\left(e^{x}\right)}^{x}}}{e}\]

  7. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{e}{{\left(e^{x}\right)}^{x}}}}\]

  8. Final simplification0.0

    \[\leadsto \frac{1}{\frac{e}{{\left(e^{x}\right)}^{x}}}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 4.5s)Debug log

sample56.0ms

Algorithm
intervals

simplify74.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

74.0ms
(exp (- (- 1 (* x x))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(exp (* x x))
0.0b
(/ (exp (* x x)) E)

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 22
Calls

2 calls. Slowest were:

3.0ms
(/ (exp (* x x)) E)
1.0ms
(exp (* x x))

series44.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

32.0ms
(/ (exp (* x x)) E)
12.0ms
(exp (* x x))

simplify55.0ms

Counts
10 → 28
Calls

10 calls. Slowest were:

26.0ms
(+ (* 1/2 (/ (pow x 4) E)) (+ (/ (pow x 2) E) (/ 1 E)))
13.0ms
(+ (pow x 2) (+ (* 1/2 (pow x 4)) 1))
4.0ms
(/ (exp (pow x 2)) E)

prune206.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (exp x) x)
0.0b
(/ (pow (exp x) x) E)

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

6.0ms
(/ (pow (exp x) x) E)
2.0ms
(pow (exp x) x)

series152.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

87.0ms
(/ (pow (exp x) x) E)
65.0ms
(pow (exp x) x)

simplify56.0ms

Counts
16 → 35
Calls

16 calls. Slowest were:

27.0ms
(+ (* 1/2 (/ (pow x 4) E)) (+ (/ (pow x 2) E) (/ 1 E)))
10.0ms
(+ (pow x 2) (+ (* 1/2 (pow x 4)) 1))
4.0ms
(/ (exp (pow x 2)) E)

prune174.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (/ E (pow (exp x) x)))
0.0b
(pow (exp x) x)
0.0b
(/ E (pow (exp x) x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

1.0ms
(pow (exp x) x)
1.0ms
(/ 1 (/ E (pow (exp x) x)))
1.0ms
(/ E (pow (exp x) x))

series151.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

62.0ms
(/ 1 (/ E (pow (exp x) x)))
50.0ms
(/ E (pow (exp x) x))
40.0ms
(pow (exp x) x)

simplify146.0ms

Counts
26 → 56
Calls

26 calls. Slowest were:

70.0ms
(- (+ (* 1/2 (* (pow x 4) E)) E) (* (pow x 2) E))
26.0ms
(+ (* 1/2 (/ (pow x 4) E)) (+ (/ (pow x 2) E) (/ 1 E)))
10.0ms
(+ (pow x 2) (+ (* 1/2 (pow x 4)) 1))

prune286.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (sqrt (/ E (pow (exp x) x)))) (sqrt (/ E (pow (exp x) x))))
0.0b
(pow (exp x) x)
0.0b
(pow (exp x) x)
0.0b
(sqrt (/ E (pow (exp x) x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 105
Calls

4 calls. Slowest were:

4.0ms
(/ (/ 1 (sqrt (/ E (pow (exp x) x)))) (sqrt (/ E (pow (exp x) x))))
1.0ms
(pow (exp x) x)
1.0ms
(sqrt (/ E (pow (exp x) x)))

series208.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

64.0ms
(/ (/ 1 (sqrt (/ E (pow (exp x) x)))) (sqrt (/ E (pow (exp x) x))))
63.0ms
(sqrt (/ E (pow (exp x) x)))
41.0ms
(pow (exp x) x)
40.0ms
(pow (exp x) x)

simplify926.0ms

Counts
118 → 117
Calls

118 calls. Slowest were:

276.0ms
(- (+ (sqrt E) (* 1/8 (* (pow x 4) (sqrt E)))) (* 1/2 (* (pow x 2) (sqrt E))))
143.0ms
(/ (* (* (/ 1 (sqrt (/ E (pow (exp x) x)))) (/ 1 (sqrt (/ E (pow (exp x) x))))) (/ 1 (sqrt (/ E (pow (exp x) x))))) (* (* (sqrt (/ E (pow (exp x) x))) (sqrt (/ E (pow (exp x) x)))) (sqrt (/ E (pow (exp x) x)))))
26.0ms
(+ (* 1/2 (/ (pow x 4) E)) (+ (/ (pow x 2) E) (/ 1 E)))

prune888.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals