Average Error: 0.0 → 0.0
Time: 23.6s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{im} + \left(0.5 \cdot \cos re\right) \cdot e^{-im}\]

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 23.0s)Debug log

sample216.0ms

Algorithm
intervals

simplify354.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

354.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

25.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
12.0ms
(+ (exp (- im)) (exp im))

series134.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

97.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
36.0ms
(+ (exp (- im)) (exp im))

simplify1.5s

Counts
19 → 38
Calls

19 calls. Slowest were:

452.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
295.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
249.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))

prune445.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

17.0ms
(+ (* (exp (- im)) (* 0.5 (cos re))) (* (exp im) (* 0.5 (cos re))))
8.0ms
(* (exp (- im)) (* 0.5 (cos re)))
5.0ms
(* (exp im) (* 0.5 (cos re)))

series229.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

113.0ms
(+ (* (exp (- im)) (* 0.5 (cos re))) (* (exp im) (* 0.5 (cos re))))
58.0ms
(* (exp im) (* 0.5 (cos re)))
58.0ms
(* (exp (- im)) (* 0.5 (cos re)))

simplify1.9s

Counts
26 → 53
Calls

26 calls. Slowest were:

394.0ms
(* (* (* (exp (- im)) (exp (- im))) (exp (- im))) (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))))
291.0ms
(+ (* 0.5 (* (exp im) (cos re))) (* 0.5 (* (exp (* -1 im)) (cos re))))
234.0ms
(* (* (* (exp im) (exp im)) (exp im)) (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))))

prune579.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (exp im))
0.1b
(cbrt (exp im))
0.1b
(cbrt (exp im))
0.0b
(* (cbrt (exp im)) (cbrt (exp im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
4 → 61
Calls

4 calls. Slowest were:

10.0ms
(* (cbrt (exp im)) (cbrt (exp im)))
1.0ms
(cbrt (exp im))
1.0ms
(cbrt (exp im))

series501.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

166.0ms
(cbrt (exp im))
126.0ms
(* (cbrt (exp im)) (cbrt (exp im)))
112.0ms
(cbrt (exp im))
97.0ms
(cbrt (exp im))

simplify258.0ms

Counts
41 → 73
Calls

41 calls. Slowest were:

42.0ms
(+ (* 1/18 (pow im 2)) (+ (* 1/3 im) 1))
40.0ms
(+ (* 2/9 (pow im 2)) (+ (* 2/3 im) 1))
40.0ms
(+ (* 1/18 (pow im 2)) (+ (* 1/3 im) 1))

prune906.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
0.2b
(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
0.0b
(sqrt (+ (exp (- im)) (exp im)))
0.0b
(sqrt (+ (exp (- im)) (exp im)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

59.0ms
(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
12.0ms
(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
7.0ms
(sqrt (+ (exp (- im)) (exp im)))

series266.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

89.0ms
(* (* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im))))
86.0ms
(* (* 0.5 (cos re)) (sqrt (+ (exp (- im)) (exp im))))
46.0ms
(sqrt (+ (exp (- im)) (exp im)))
44.0ms
(sqrt (+ (exp (- im)) (exp im)))

simplify5.7s

Counts
64 → 93
Calls

64 calls. Slowest were:

707.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (sqrt (+ (exp (- im)) (exp im))) (sqrt (+ (exp (- im)) (exp im)))) (sqrt (+ (exp (- im)) (exp im)))))
350.0ms
(- (+ (sqrt 2) (+ (* 1/2 (/ (pow im 2) (sqrt 2))) (* 1/24 (/ (pow im 4) (sqrt 2))))) (* 1/8 (/ (pow im 4) (pow (sqrt 2) 3))))
339.0ms
(- (+ (sqrt 2) (+ (* 1/2 (/ (pow im 2) (sqrt 2))) (* 1/24 (/ (pow im 4) (sqrt 2))))) (* 1/8 (/ (pow im 4) (pow (sqrt 2) 3))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes203.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.5s

Algorithm
intervals