Average Error: 0.0 → 0.0
Time: 19.0s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]

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

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018362 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 6.0s)Debug log

start434.0ms

Algorithm
intervals

setup371.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 0.5 (exp im))
0.0b
(+ (* 0.5 (exp im)) (/ 0.5 (exp im)))
0.0b
(* (sin re) (+ (* 0.5 (exp im)) (/ 0.5 (exp im))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

15.0ms
(* (sin re) (+ (* 0.5 (exp im)) (/ 0.5 (exp im))))
7.0ms
(+ (* 0.5 (exp im)) (/ 0.5 (exp im)))
5.0ms
(/ 0.5 (exp im))

series225.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

127.0ms
(* (sin re) (+ (* 0.5 (exp im)) (/ 0.5 (exp im))))
68.0ms
(+ (* 0.5 (exp im)) (/ 0.5 (exp im)))
29.0ms
(/ 0.5 (exp im))

simplify1.8s

Counts
27 → 56
Calls

27 calls. Slowest were:

475.0ms
(* (sin re) (+ (* 0.5 (exp im)) (* 0.5 (/ 1 (exp im)))))
444.0ms
(* (sin re) (+ (* 0.5 (exp im)) (* 0.5 (/ 1 (exp im)))))
390.0ms
(+ (* (* 0.5 (exp im)) (* 0.5 (exp im))) (- (* (/ 0.5 (exp im)) (/ 0.5 (exp im))) (* (* 0.5 (exp im)) (/ 0.5 (exp im)))))

prune653.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sin re) (/ 0.5 (exp im)))
0.0b
(/ 0.5 (exp im))
0.0b
(+ (* (sin re) (* 0.5 (exp im))) (* (sin re) (/ 0.5 (exp im))))
0.0b
(* (sin re) (* 0.5 (exp im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

8.0ms
(+ (* (sin re) (* 0.5 (exp im))) (* (sin re) (/ 0.5 (exp im))))
5.0ms
(* (sin re) (* 0.5 (exp im)))
4.0ms
(* (sin re) (/ 0.5 (exp im)))

series214.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

106.0ms
(+ (* (sin re) (* 0.5 (exp im))) (* (sin re) (/ 0.5 (exp im))))
62.0ms
(* (sin re) (* 0.5 (exp im)))
37.0ms
(* (sin re) (/ 0.5 (exp im)))
10.0ms
(/ 0.5 (exp im))

simplify1.3s

Counts
34 → 71
Calls

34 calls. Slowest were:

250.0ms
(- (+ (* 0.5 re) (* 0.5 (* re im))) (* 0.08333333333333333 (pow re 3)))
249.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))
200.0ms
(* (* (* (sin re) (sin re)) (sin re)) (* (* (* 0.5 (exp im)) (* 0.5 (exp im))) (* 0.5 (exp im))))

prune780.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms