Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Initial simplification0.0

    \[\leadsto 0.5 \cdot (\left(e^{im}\right) \cdot \left(\sin re\right) + \left(\frac{\sin re}{e^{im}}\right))_*\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 4.9s)Debug log

start371.0ms

Algorithm
intervals

setup590.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (sin re) (exp im))
0.0b
(fma (exp im) (sin re) (/ (sin re) (exp im)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 39
Calls

2 calls. Slowest were:

3.0ms
(/ (sin re) (exp im))
0.0ms
(fma (exp im) (sin re) (/ (sin re) (exp im)))

series143.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

91.0ms
(fma (exp im) (sin re) (/ (sin re) (exp im)))
52.0ms
(/ (sin re) (exp im))

simplify797.0ms

Counts
31 → 45
Calls

31 calls. Slowest were:

292.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))
283.0ms
(- re (+ (* re im) (* 1/6 (pow re 3))))
127.0ms
(/ (* (* (sin re) (sin re)) (sin re)) (* (* (exp im) (exp im)) (exp im)))

prune500.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (sin re) (exp im))
0.0b
(+ (* (exp im) (sin re)) (/ (sin re) (exp im)))
0.0b
(* (exp im) (sin re))

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
3 → 62
Calls

3 calls. Slowest were:

12.0ms
(+ (* (exp im) (sin re)) (/ (sin re) (exp im)))
7.0ms
(* (exp im) (sin re))
3.0ms
(/ (sin re) (exp im))

series240.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

118.0ms
(+ (* (exp im) (sin re)) (/ (sin re) (exp im)))
67.0ms
(* (exp im) (sin re))
55.0ms
(/ (sin re) (exp im))

simplify1.1s

Counts
44 → 71
Calls

44 calls. Slowest were:

314.0ms
(+ (* re im) (+ re (* 1/2 (* re (pow im 2)))))
265.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))
222.0ms
(- re (+ (* re im) (* 1/6 (pow re 3))))

prune905.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes145.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms