Average Error: 58.7 → 0.0
Time: 3.6s
Precision: 64
Internal Precision: 128
\[e^{x} - 1\]
↓
\[(e^{x} - 1)^*\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original58.7
Target0.5
Herbie0.0
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right)\]

Derivation

  1. Initial program 58.7

    \[e^{x} - 1\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (x)
  :name "expm1 (example 3.7)"
  :pre (< -0.00017 x)

  :herbie-target
  (* x (+ (+ 1 (/ x 2)) (/ (* x x) 6)))

  (- (exp x) 1))

Details

Time bar (total: 3.3s)Debug log

sample106.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

5.0ms
(- (exp x) 1)

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(expm1 x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(expm1 x)

series19.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

19.0ms
(expm1 x)

simplify223.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

217.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
3.0ms
(- (exp x) 1)
2.0ms
(- (exp x) 1)

prune91.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

5.2b
(- (exp x) 1)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 18
Calls

1 calls. Slowest were:

5.0ms
(- (exp x) 1)

series11.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

11.0ms
(- (exp x) 1)

simplify201.0ms

Counts
6 → 21
Calls

6 calls. Slowest were:

188.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
5.0ms
(- (exp x) 1)
4.0ms
(- (exp x) 1)

prune118.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

end0.0ms

sample2.4s

Algorithm
intervals