Average Error: 0.0 → 0.0
Time: 21.8s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5}{e^{im}} \cdot \sin re\]

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 21.3s)Debug log

sample325.0ms

Algorithm
intervals

simplify609.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

608.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

15.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
6.0ms
(+ (exp (- 0 im)) (exp im))

series134.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

90.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
44.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.8s

Counts
19 → 38
Calls

19 calls. Slowest were:

378.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
376.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
314.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
3 → 46
Calls

3 calls. Slowest were:

17.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
13.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
10.0ms
(* (exp im) (* 0.5 (sin re)))

series266.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

146.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
71.0ms
(* (exp im) (* 0.5 (sin re)))
49.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))

simplify2.7s

Counts
28 → 55
Calls

28 calls. Slowest were:

409.0ms
(* (exp (* (exp (- 0 im)) (* 0.5 (sin re)))) (exp (* (exp im) (* 0.5 (sin re)))))
389.0ms
(* (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
347.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))

prune629.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 58
Calls

4 calls. Slowest were:

15.0ms
(+ (* (sin re) (/ 0.5 (exp im))) (* (exp im) (* 0.5 (sin re))))
10.0ms
(* (exp im) (* 0.5 (sin re)))
7.0ms
(* (sin re) (/ 0.5 (exp im)))

series234.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

131.0ms
(+ (* (sin re) (/ 0.5 (exp im))) (* (exp im) (* 0.5 (sin re))))
45.0ms
(* (exp im) (* 0.5 (sin re)))
39.0ms
(* (sin re) (/ 0.5 (exp im)))
18.0ms
(/ 0.5 (exp im))

simplify1.4s

Counts
32 → 70
Calls

32 calls. Slowest were:

276.0ms
(* (* (* (exp im) (exp im)) (exp im)) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
227.0ms
(+ (* 0.5 (* re im)) (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))))
221.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))

prune625.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 84
Calls

4 calls. Slowest were:

8.0ms
(* (sin re) (/ (/ 0.5 (sqrt (exp im))) (sqrt (exp im))))
5.0ms
(* (exp im) (* 0.5 (sin re)))
1.0ms
(sqrt (exp im))

series136.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

60.0ms
(* (exp im) (* 0.5 (sin re)))
40.0ms
(* (sin re) (/ (/ 0.5 (sqrt (exp im))) (sqrt (exp im))))
23.0ms
(sqrt (exp im))
13.0ms
(sqrt (exp im))

simplify1.8s

Counts
62 → 96
Calls

62 calls. Slowest were:

288.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))
283.0ms
(* (* (* (sin re) (sin re)) (sin re)) (* (* (/ (/ 0.5 (sqrt (exp im))) (sqrt (exp im))) (/ (/ 0.5 (sqrt (exp im))) (sqrt (exp im)))) (/ (/ 0.5 (sqrt (exp im))) (sqrt (exp im)))))
236.0ms
(+ (* 0.5 (* re im)) (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))))

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes260.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.8s

Algorithm
intervals