Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{e^{1 - x \cdot x}}\]

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. Using strategy rm

  3. Applied add-log-exp0.0

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

  4. Applied neg-log0.0

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

  5. Applied rem-exp-log0.0

    \[\leadsto \color{blue}{\frac{1}{e^{1 - x \cdot x}}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{e^{1 - x \cdot x}}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 10.6s)Debug log

start33.0ms

Algorithm
intervals

setup87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 23
Calls

1 calls. Slowest were:

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

series17.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify373.0ms

Counts
17 → 26
Calls

17 calls. Slowest were:

155.0ms
(+ (exp -1) (+ (* (pow x 2) (exp -1)) (* 1/2 (* (pow x 4) (exp -1)))))
43.0ms
(exp (* (cbrt (- (- 1 (* x x)))) (cbrt (- (- 1 (* x x))))))
41.0ms
(exp (sqrt (- (- 1 (* x x)))))

prune248.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
2 → 36
Calls

2 calls. Slowest were:

3.0ms
(/ 1 (exp (- 1 (* x x))))
3.0ms
(exp (- 1 (* x x)))

series67.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

42.0ms
(/ 1 (exp (- 1 (* x x))))
25.0ms
(exp (- 1 (* x x)))

simplify466.0ms

Counts
23 → 42
Calls

23 calls. Slowest were:

105.0ms
(/ 1 (exp (- 1 (pow x 2))))
90.0ms
(- (+ (* 1/2 (* (pow x 4) E)) E) (* (pow x 2) E))
72.0ms
(/ 1 (exp (- 1 (pow x 2))))

prune335.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b
(cbrt (exp (- 1 (* x x))))
1.6b
(cbrt (exp (- 1 (* x x))))
1.6b
(cbrt (exp (- 1 (* x x))))
1.0b
(* (cbrt (exp (- 1 (* x x)))) (cbrt (exp (- 1 (* x x)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 77
Calls

4 calls. Slowest were:

13.0ms
(* (cbrt (exp (- 1 (* x x)))) (cbrt (exp (- 1 (* x x)))))
3.0ms
(cbrt (exp (- 1 (* x x))))
3.0ms
(cbrt (exp (- 1 (* x x))))

series708.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

220.0ms
(* (cbrt (exp (- 1 (* x x)))) (cbrt (exp (- 1 (* x x)))))
173.0ms
(cbrt (exp (- 1 (* x x))))
165.0ms
(cbrt (exp (- 1 (* x x))))
150.0ms
(cbrt (exp (- 1 (* x x))))

simplify3.2s

Counts
58 → 89
Calls

58 calls. Slowest were:

452.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))
431.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))
413.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))

prune625.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(cbrt (exp (- 1 (* x x))))
1.6b
(cbrt (exp (- 1 (* x x))))
1.6b
(cbrt (exp (- 1 (* x x))))
1.6b
(cbrt (exp (- 1 (* x x))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

4.0ms
(cbrt (exp (- 1 (* x x))))
1.0ms
(cbrt (exp (- 1 (* x x))))
1.0ms
(cbrt (exp (- 1 (* x x))))

series696.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

191.0ms
(cbrt (exp (- 1 (* x x))))
184.0ms
(cbrt (exp (- 1 (* x x))))
168.0ms
(cbrt (exp (- 1 (* x x))))
152.0ms
(cbrt (exp (- 1 (* x x))))

simplify2.9s

Counts
36 → 68
Calls

36 calls. Slowest were:

850.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))
501.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))
422.0ms
(- (+ (exp 1/3) (* 1/18 (* (pow x 4) (exp 1/3)))) (* 1/3 (* (pow x 2) (exp 1/3))))

prune615.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms