Average Error: 0.0 → 0.0
Time: 21.2s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{\log \left(e^{im} + e^{-im}\right)} \cdot \left(0.5 \cdot \cos re\right)\]

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. Using strategy rm

  3. Applied add-exp-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 20.7s)Debug log

sample294.0ms

Algorithm
intervals

simplify388.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

388.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

22.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
6.0ms
(+ (exp (- im)) (exp im))

series109.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

71.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
38.0ms
(+ (exp (- im)) (exp im))

simplify1.4s

Counts
19 → 38
Calls

19 calls. Slowest were:

394.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
263.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
215.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))

prune420.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

34.0ms
(* (* 0.5 (cos re)) (exp (log (+ (exp (- im)) (exp im)))))
12.0ms
(+ (exp (- im)) (exp im))
9.0ms
(log (+ (exp (- im)) (exp im)))

series219.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

103.0ms
(log (+ (exp (- im)) (exp im)))
76.0ms
(* (* 0.5 (cos re)) (exp (log (+ (exp (- im)) (exp im)))))
40.0ms
(+ (exp (- im)) (exp im))

simplify1.6s

Counts
30 → 57
Calls

30 calls. Slowest were:

340.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
300.0ms
(* (* 0.5 (cos re)) (exp (log (+ (exp (- im)) (exp im)))))
249.0ms
(log (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im))))

prune795.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im)))))) (sqrt (+ (exp im) (exp (- im)))))
0.2b
(* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im))))))
0.0b
(+ (exp (- im)) (exp im))
0.0b
(log (+ (exp (- im)) (exp im)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

54.0ms
(* (* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im)))))) (sqrt (+ (exp im) (exp (- im)))))
33.0ms
(* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im))))))
11.0ms
(+ (exp (- im)) (exp im))

series309.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

109.0ms
(* (* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im)))))) (sqrt (+ (exp im) (exp (- im)))))
92.0ms
(* (* 0.5 (cos re)) (sqrt (exp (log (+ (exp (- im)) (exp im))))))
80.0ms
(log (+ (exp (- im)) (exp im)))
28.0ms
(+ (exp (- im)) (exp im))

simplify4.8s

Counts
62 → 93
Calls

62 calls. Slowest were:

658.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (sqrt (exp (log (+ (exp (- im)) (exp im))))) (sqrt (exp (log (+ (exp (- im)) (exp im)))))) (sqrt (exp (log (+ (exp (- im)) (exp im)))))))
431.0ms
(* (sqrt (exp (log (+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))))) (sqrt (+ (* (exp im) (exp im)) (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp (- im)))))))
320.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))

prune1.4s

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

bsearch3.0ms

end0.0ms

sample8.6s

Algorithm
intervals