Average Error: 0.0 → 0.0
Time: 24.3s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 12.4s)Debug log

start380.0ms

Algorithm
intervals

setup127.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
3 → 55
Calls

3 calls. Slowest were:

6.0ms
(+ (* (exp im) (sin re)) (/ (sin re) (exp im)))
5.0ms
(/ (sin re) (exp im))
4.0ms
(* (exp im) (sin re))

series244.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

96.0ms
(+ (* (exp im) (sin re)) (/ (sin re) (exp im)))
78.0ms
(* (exp im) (sin re))
70.0ms
(/ (sin re) (exp im))

simplify549.0ms

Counts
43 → 64
Calls

43 calls. Slowest were:

98.0ms
(/ (* (* (sin re) (sin re)) (sin re)) (* (* (exp im) (exp im)) (exp im)))
98.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))
89.0ms
(- re (+ (* re im) (* 1/6 (pow re 3))))

prune694.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
1 → 20
Calls

1 calls. Slowest were:

14.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series83.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

83.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify742.0ms

Counts
14 → 23
Calls

14 calls. Slowest were:

133.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (+ (exp (- 0 im)) (exp im)) (+ (exp (- 0 im)) (exp im))) (+ (exp (- 0 im)) (exp im))))
115.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))
114.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))

prune327.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 243
Calls

4 calls. Slowest were:

7.0ms
(/ (/ (sin re) (sqrt (exp im))) (sqrt (exp im)))
3.0ms
(/ (sin re) (sqrt (exp im)))
3.0ms
(* (exp im) (sin re))

series228.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

81.0ms
(/ (sin re) (sqrt (exp im)))
71.0ms
(* (exp im) (sin re))
55.0ms
(/ (/ (sin re) (sqrt (exp im))) (sqrt (exp im)))
21.0ms
(sqrt (exp im))

simplify5.3s

Counts
366 → 255
Calls

366 calls. Slowest were:

439.0ms
(/ (* (* (/ (sin re) (sqrt (exp im))) (/ (sin re) (sqrt (exp im)))) (/ (sin re) (sqrt (exp im)))) (* (* (sqrt (exp im)) (sqrt (exp im))) (sqrt (exp im))))
183.0ms
(/ (/ (* (* (sin re) (sin re)) (sin re)) (* (* (sqrt (exp im)) (sqrt (exp im))) (sqrt (exp im)))) (* (* (sqrt (exp im)) (sqrt (exp im))) (sqrt (exp im))))
170.0ms
(/ (* (* (sin re) (sin re)) (sin re)) (* (* (sqrt (exp im)) (sqrt (exp im))) (sqrt (exp im))))

prune3.4s

Pruning

2 alts after pruning (0 fresh and 2 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

bsearch2.0ms