Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{re} \cdot \cos im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)} \cdot \cos im\]

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 7.3s)Debug log

sample107.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

4.0ms
(* (exp re) (cos im))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (exp re) (cos im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

8.0ms
(* (exp re) (cos im))

series55.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

55.0ms
(* (exp re) (cos im))

simplify170.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

95.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
54.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune178.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
0.0b
(* (sqrt (exp re)) (cos im))
0.0b
(sqrt (exp re))
0.0b
(sqrt (exp re))

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

22.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
8.0ms
(* (sqrt (exp re)) (cos im))
1.0ms
(sqrt (exp re))

series153.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

74.0ms
(* (sqrt (exp re)) (cos im))
52.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
15.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.1s

Counts
43 → 85
Calls

43 calls. Slowest were:

410.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
391.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
66.0ms
(+ (* 1/2 re) (+ (* 1/8 (pow re 2)) 1))

prune704.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b
(log1p (* (exp re) (cos im)))
0.1b
(expm1 (log1p (* (exp re) (cos im))))
0.0b
(* (exp re) (cos im))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
3 → 41
Calls

3 calls. Slowest were:

4.0ms
(* (exp re) (cos im))
0.0ms
(log1p (* (exp re) (cos im)))
0.0ms
(expm1 (log1p (* (exp re) (cos im))))

series209.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

89.0ms
(log1p (* (exp re) (cos im)))
87.0ms
(expm1 (log1p (* (exp re) (cos im))))
33.0ms
(* (exp re) (cos im))

simplify277.0ms

Counts
19 → 50
Calls

19 calls. Slowest were:

83.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
66.0ms
(+ (log 2) (+ (* 1/2 re) (* 1/8 (pow re 2))))
55.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))

prune499.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.5s

Algorithm
intervals