Average Error: 0.0 → 0.0
Time: 21.0s
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 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 20.6s)Debug log

sample269.0ms

Algorithm
intervals

simplify308.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

307.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
2 → 39
Calls

2 calls. Slowest were:

26.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
18.0ms
(+ (exp (- im)) (exp im))

series123.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

91.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
32.0ms
(+ (exp (- im)) (exp im))

simplify1.5s

Counts
21 → 45
Calls

21 calls. Slowest were:

484.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
271.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))
223.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune449.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Counts
3 → 52
Calls

3 calls. Slowest were:

23.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
15.0ms
(* (* 0.5 (cos re)) (exp (- im)))
10.0ms
(* (* 0.5 (cos re)) (exp im))

series212.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

119.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
50.0ms
(* (* 0.5 (cos re)) (exp (- im)))
43.0ms
(* (* 0.5 (cos re)) (exp im))

simplify2.7s

Counts
28 → 61
Calls

28 calls. Slowest were:

520.0ms
(+ (* 0.5 (* (exp (- im)) (cos re))) (* 0.5 (* (exp im) (cos re))))
457.0ms
(+ (* 0.5 (* (exp im) (cos re))) (* 0.5 (* (exp (* -1 im)) (cos re))))
346.0ms
(* (exp (* (* 0.5 (cos re)) (exp (- im)))) (exp (* (* 0.5 (cos re)) (exp im))))

prune626.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (exp im) 3)
0.0b
(fma (exp (- im)) (exp (- im)) (expm1 (+ im im)))
0.0b
(pow (exp (- im)) 3)
0.0b
(/ (* (* 0.5 (cos re)) (+ (pow (exp (- im)) 3) (pow (exp im) 3))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 83
Calls

4 calls. Slowest were:

18.0ms
(/ (* (* 0.5 (cos re)) (+ (pow (exp (- im)) 3) (pow (exp im) 3))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))
2.0ms
(pow (exp (- im)) 3)
1.0ms
(pow (exp im) 3)

series310.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

216.0ms
(/ (* (* 0.5 (cos re)) (+ (pow (exp (- im)) 3) (pow (exp im) 3))) (fma (exp (- im)) (exp (- im)) (expm1 (+ im im))))
63.0ms
(fma (exp (- im)) (exp (- im)) (expm1 (+ im im)))
16.0ms
(pow (exp (- im)) 3)
15.0ms
(pow (exp im) 3)

simplify4.0s

Counts
52 → 95
Calls

52 calls. Slowest were:

630.0ms
(* (* 0.5 (cos re)) (- (* (pow (exp (- im)) 3) (pow (exp (- im)) 3)) (* (pow (exp im) 3) (pow (exp im) 3))))
536.0ms
(* (* 0.5 (cos re)) (+ (pow (pow (exp (- im)) 3) 3) (pow (pow (exp im) 3) 3)))
326.0ms
(* 0.5 (/ (* (+ (pow (exp (* -1 im)) 3) (pow (exp im) 3)) (cos re)) (- (+ (exp (* 2 im)) (pow (exp (* -1 im)) 2)) 1)))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes270.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample8.3s

Algorithm
intervals