Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-\left(1 - x \cdot x\right)}\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 6.4s)Debug log

sample70.0ms

Algorithm
intervals
Results
526×(pre true 80)
526×(body real 80)

simplify96.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
95.0ms
(exp (- (- 1 (* x x))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
10×exp-prod
4×add-cube-cbrt
4×*-un-lft-identity
4×add-sqr-sqrt
3×add-log-exp
3×distribute-rgt-neg-in
3×distribute-lft-neg-in
2×rem-exp-log
2×exp-sum
2×distribute-neg-in
1×add-exp-log
1×neg-log
1×exp-diff
1×add-cbrt-cube
1×sub-neg
1×neg-mul-1
1×pow1
1×exp-neg
1×neg-sub0
Counts
1 → 23
Calls
1 calls:
Slowest
6.0ms
(exp (- (- 1 (* x x))))

series27.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
26.0ms
(exp (- (- 1 (* x x))))

simplify235.0ms

Counts
17 → 26
Calls
17 calls:
Slowest
88.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
27.0ms
(exp (* (cbrt (- (- 1 (* x x)))) (cbrt (- (- 1 (* x x))))))
25.0ms
(exp (sqrt (- (- 1 (* x x)))))
16.0ms
(- (- 1 (* x x)))
13.0ms
(exp (- (pow x 2) 1))

prune224.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (exp (- (- 1 (* x x)))))
1.0b
(cbrt (exp (- (- 1 (* x x)))))
1.0b
(cbrt (exp (- (- 1 (* x x)))))
0.0b
(* (cbrt (exp (- (- 1 (* x x))))) (cbrt (exp (- (- 1 (* x x))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
18×cbrt-div
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
10×exp-sum
10×distribute-neg-in
9×exp-diff
9×pow1
9×exp-neg
9×neg-sub0
8×associate-*l*
8×associate-*r*
7×pow1/3
6×add-exp-log
5×sub-neg
4×add-log-exp
4×add-cbrt-cube
4×frac-times
2×pow-prod-up
2×associate-*r/
2×associate-*l/
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 85
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (exp (- (- 1 (* x x))))) (cbrt (exp (- (- 1 (* x x))))))
3.0ms
(cbrt (exp (- (- 1 (* x x)))))
3.0ms
(cbrt (exp (- (- 1 (* x x)))))
3.0ms
(cbrt (exp (- (- 1 (* x x)))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(* (cbrt (exp (- (- 1 (* x x))))) (cbrt (exp (- (- 1 (* x x))))))
170.0ms
(cbrt (exp (- (- 1 (* x x)))))
145.0ms
(cbrt (exp (- (- 1 (* x x)))))
124.0ms
(cbrt (exp (- (- 1 (* x x)))))

simplify3.2s

Counts
69 → 97
Calls
69 calls:
Slowest
210.0ms
(* (exp (- (- 1 (* x x)))) (exp (- (- 1 (* x x)))))
201.0ms
(pow (pow (exp (- (pow x 2) 1)) 2) 1/3)
194.0ms
(pow (pow (exp (- (pow x 2) 1)) 2) 1/3)
160.0ms
(* (exp (- (- 1 (* x x)))) (exp (- (- 1 (* x x)))))
110.0ms
(+ (* 1/18 (* (pow x 4) (exp -1/3))) (+ (exp -1/3) (* 1/3 (* (pow x 2) (exp -1/3)))))

prune596.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
15949×(pre true 80)
15949×(body real 80)