Average Error: 0.0 → 0.0
Time: 9.3s
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 2019008 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 8.8s)Debug log

sample105.0ms

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

localize46.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series62.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

61.0ms
(* (exp re) (cos im))

simplify123.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

56.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
47.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune213.0ms

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

11.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
6.0ms
(* (sqrt (exp re)) (cos im))
1.0ms
(sqrt (exp re))

series122.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

57.0ms
(* (sqrt (exp re)) (cos im))
35.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (cos im)))
18.0ms
(sqrt (exp re))
11.0ms
(sqrt (exp re))

simplify1.1s

Counts
43 → 77
Calls

43 calls. Slowest were:

468.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (cos im)) (* (sqrt (exp re)) (cos im))) (* (sqrt (exp re)) (cos im))))
372.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im))))
55.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (cos im) (cos im)) (cos im)))

prune651.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos im) 3)
0.2b
(cbrt (* (pow (exp re) 3) (pow (cos im) 3)))
0.0b
(pow (exp re) 3)
0.0b
(* (pow (exp re) 3) (pow (cos im) 3))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 89
Calls

4 calls. Slowest were:

7.0ms
(* (pow (exp re) 3) (pow (cos im) 3))
5.0ms
(cbrt (* (pow (exp re) 3) (pow (cos im) 3)))
2.0ms
(pow (cos im) 3)

series158.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

59.0ms
(* (pow (exp re) 3) (pow (cos im) 3))
54.0ms
(cbrt (* (pow (exp re) 3) (pow (cos im) 3)))
23.0ms
(pow (exp re) 3)
21.0ms
(pow (cos im) 3)

simplify1.1s

Counts
64 → 101
Calls

64 calls. Slowest were:

390.0ms
(* (* (* (pow (exp re) 3) (pow (exp re) 3)) (pow (exp re) 3)) (* (* (pow (cos im) 3) (pow (cos im) 3)) (pow (cos im) 3)))
47.0ms
(+ (log (pow (exp re) 3)) (* (log (cos im)) 3))
45.0ms
(+ (log (pow (exp re) 3)) (log (pow (cos im) 3)))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes202.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals