Average Error: 0.0 → 0.0
Time: 7.8s
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 2019004 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 7.4s)Debug log

sample105.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(* (exp re) (cos im))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series71.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

71.0ms
(* (exp re) (cos im))

simplify149.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

86.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
42.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (cos im) (exp re))

prune203.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

15.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
4.0ms
(* (sqrt (exp re)) (cos im))
1.0ms
(sqrt (exp re))

series129.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

48.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
42.0ms
(* (sqrt (exp re)) (cos im))
20.0ms
(sqrt (exp re))
19.0ms
(sqrt (exp re))

simplify1.1s

Counts
43 → 77
Calls

43 calls. Slowest were:

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))))
373.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
64.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im)))

prune735.0ms

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
3 → 41
Calls

3 calls. Slowest were:

4.0ms
(* (exp re) (cos im))
3.0ms
(exp (* (exp re) (cos im)))
2.0ms
(log (exp (* (exp re) (cos im))))

series116.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

50.0ms
(exp (* (exp re) (cos im)))
33.0ms
(log (exp (* (exp re) (cos im))))
33.0ms
(* (exp re) (cos im))

simplify198.0ms

Counts
26 → 50
Calls

26 calls. Slowest were:

53.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
45.0ms
(+ (* (pow re 2) E) (+ (* re E) E))
41.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))

prune525.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.9s

Algorithm
intervals