Average Error: 0.0 → 0.0
Time: 16.8s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]

Reproduce

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

Details

Time bar (total: 16.3s)Debug log

sample230.0ms

Algorithm
intervals

simplify494.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

493.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
0.0b
(+ (exp (- im)) (exp im))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

12.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
8.0ms
(+ (exp (- im)) (exp im))

series104.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

64.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
40.0ms
(+ (exp (- im)) (exp im))

simplify1.3s

Counts
19 → 38
Calls

19 calls. Slowest were:

396.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
276.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
164.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))

prune372.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (exp (- im)) (* 0.5 (cos re)))
0.0b
(* (exp im) (* 0.5 (cos re)))
0.0b
(+ (* (exp (- im)) (* 0.5 (cos re))) (* (exp im) (* 0.5 (cos re))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

24.0ms
(+ (* (exp (- im)) (* 0.5 (cos re))) (* (exp im) (* 0.5 (cos re))))
11.0ms
(* (exp (- im)) (* 0.5 (cos re)))
10.0ms
(* (exp im) (* 0.5 (cos re)))

series235.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

124.0ms
(+ (* (exp (- im)) (* 0.5 (cos re))) (* (exp im) (* 0.5 (cos re))))
59.0ms
(* (exp (- im)) (* 0.5 (cos re)))
52.0ms
(* (exp im) (* 0.5 (cos re)))

simplify2.0s

Counts
26 → 53
Calls

26 calls. Slowest were:

373.0ms
(* (* (* (exp (- im)) (exp (- im))) (exp (- im))) (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))))
373.0ms
(+ (* 0.5 (* (exp im) (cos re))) (* 0.5 (* (exp (* -1 im)) (cos re))))
265.0ms
(* (exp (* (exp (- im)) (* 0.5 (cos re)))) (exp (* (exp im) (* 0.5 (cos re)))))

prune575.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.5 (/ (exp im) (cos re)))
0.1b
(/ (exp im) (cos re))
0.0b
(* (exp im) (* 0.5 (cos re)))
0.0b
(+ (/ 0.5 (/ (exp im) (cos re))) (* (exp im) (* 0.5 (cos re))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 77
Calls

4 calls. Slowest were:

12.0ms
(+ (/ 0.5 (/ (exp im) (cos re))) (* (exp im) (* 0.5 (cos re))))
10.0ms
(* (exp im) (* 0.5 (cos re)))
6.0ms
(/ (exp im) (cos re))

series217.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

79.0ms
(+ (/ 0.5 (/ (exp im) (cos re))) (* (exp im) (* 0.5 (cos re))))
66.0ms
(/ 0.5 (/ (exp im) (cos re)))
37.0ms
(* (exp im) (* 0.5 (cos re)))
36.0ms
(/ (exp im) (cos re))

simplify880.0ms

Counts
58 → 89
Calls

58 calls. Slowest were:

280.0ms
(* (* (* (exp im) (exp im)) (exp im)) (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))))
176.0ms
(/ (* (* (exp im) (exp im)) (exp im)) (* (* (cos re) (cos re)) (cos re)))
58.0ms
(- (+ (* 0.25 (pow im 2)) 0.5) (* 0.5 im))

prune917.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample8.7s

Algorithm
intervals