Average Error: 0.0 → 0.0
Time: 14.1s
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 2018365 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 9.5s)Debug log

start105.0ms

Algorithm
intervals

setup21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

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

series69.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

69.0ms
(* (exp re) (cos im))

simplify135.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

71.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
46.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (exp re) (cos im))

prune266.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
0.2b
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
0.1b
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
0.0b
(* (exp re) (cos im))

rewrite134.0ms

Algorithm
rewrite-expression-head
Counts
4 → 126
Calls

4 calls. Slowest were:

55.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
46.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
20.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))

series208.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

65.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
56.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
50.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
37.0ms
(* (exp re) (cos im))

simplify6.7s

Counts
114 → 138
Calls

114 calls. Slowest were:

826.0ms
(* (* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))))
639.0ms
(* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
586.0ms
(* (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))))

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes186.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms