Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[e^{re} \cdot \cos im\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 2.4s)Debug log

start87.0ms

Algorithm
intervals

setup34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

7.0ms
(* (cos im) (exp re))

series51.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

51.0ms
(* (cos im) (exp re))

simplify93.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

56.0ms
(* (* (* (cos im) (cos im)) (cos im)) (* (* (exp re) (exp re)) (exp re)))
22.0ms
(- (+ re 1) (* 1/2 (pow im 2)))
3.0ms
(+ (log (cos im)) re)

prune145.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
0.0b
(* (cos im) (sqrt (exp re)))
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
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
4.0ms
(* (cos im) (sqrt (exp re)))
1.0ms
(sqrt (exp re))

series123.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

50.0ms
(* (* (cos im) (sqrt (exp re))) (sqrt (exp re)))
48.0ms
(* (cos im) (sqrt (exp re)))
13.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify982.0ms

Counts
44 → 77
Calls

44 calls. Slowest were:

429.0ms
(* (* (* (* (cos im) (sqrt (exp re))) (* (cos im) (sqrt (exp re)))) (* (cos im) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
312.0ms
(* (* (* (* (cos im) (cos im)) (cos im)) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re)))) (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))))
46.0ms
(- (+ (* 1/2 re) 1) (* 1/2 (pow im 2)))

prune659.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms