Average Error: 58.8 → 0.0
Time: 2.8s
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

Original58.8
Target0.5
Herbie0.0
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right)\]

Derivation

  1. Initial program 58.8

    \[e^{x} - 1\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 +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: 2.6s)Debug log

sample52.0ms

Algorithm
intervals
Results
366×(pre true 80)
112×(body real 1280)
110×(body real 80)
79×(body real 640)
44×(body real 320)
21×(body real 160)

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(- (exp x) 1)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize3.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.5s

Algorithm
intervals
Results
11928×(pre true 80)
4111×(body real 80)
3468×(body real 1280)
2488×(body real 640)
1225×(body real 320)
636×(body real 160)