Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]

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. Final simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 8.4s)Debug log

sample135.0ms

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

localize18.0ms

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))

series38.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

38.0ms
(* (exp re) (cos im))

simplify111.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

66.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
28.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune153.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

21.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
9.0ms
(* (sqrt (exp re)) (cos im))
1.0ms
(sqrt (exp re))

series109.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

41.0ms
(* (sqrt (exp re)) (cos im))
34.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
17.0ms
(sqrt (exp re))
16.0ms
(sqrt (exp re))

simplify1.2s

Counts
43 → 85
Calls

43 calls. Slowest were:

444.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
369.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
88.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im)))

prune904.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (sqrt (exp re)))
0.3b
(cbrt (sqrt (exp re)))
0.3b
(cbrt (sqrt (exp re)))
0.0b
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 84
Calls

4 calls. Slowest were:

6.0ms
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))
1.0ms
(cbrt (sqrt (exp re)))
1.0ms
(cbrt (sqrt (exp re)))

series452.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

128.0ms
(cbrt (sqrt (exp re)))
116.0ms
(* (cbrt (sqrt (exp re))) (cbrt (sqrt (exp re))))
112.0ms
(cbrt (sqrt (exp re)))
95.0ms
(cbrt (sqrt (exp re)))

simplify252.0ms

Counts
56 → 96
Calls

56 calls. Slowest were:

64.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
39.0ms
(+ (* 1/6 re) (+ (* 1/72 (pow re 2)) 1))
36.0ms
(+ (* 1/6 re) (+ (* 1/72 (pow re 2)) 1))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes240.0ms

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