Average Error: 0.0 → 0.0
Time: 26.1s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \left(0.5 \cdot \sin re\right) \cdot e^{-im}\]

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-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 +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: 25.0s)Debug log

sample384.0ms

Algorithm
intervals

simplify448.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

448.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite36.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

22.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
13.0ms
(+ (exp (- 0 im)) (exp im))

series129.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

84.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
45.0ms
(+ (exp (- 0 im)) (exp im))

simplify2.4s

Counts
23 → 47
Calls

23 calls. Slowest were:

532.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
461.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
419.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))

prune461.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
3 → 54
Calls

3 calls. Slowest were:

10.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
7.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
5.0ms
(* (* 0.5 (sin re)) (exp im))

series219.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

115.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
60.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
44.0ms
(* (* 0.5 (sin re)) (exp im))

simplify3.8s

Counts
30 → 63
Calls

30 calls. Slowest were:

736.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
678.0ms
(+ (* 0.5 (* (exp (- im)) (sin re))) (* 0.5 (* (sin re) (exp im))))
510.0ms
(- (+ (* 0.5 re) (* 0.5 (* re im))) (* 0.08333333333333333 (pow re 3)))

prune683.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (+ (exp (- im)) (exp im)))
1.0b
(cbrt (+ (exp (- 0 im)) (exp im)))
1.0b
(cbrt (+ (exp (- 0 im)) (exp im)))
0.5b
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

53.0ms
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))
8.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
6.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))

series686.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

178.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
173.0ms
(* (* 0.5 (sin re)) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))))
170.0ms
(cbrt (+ (exp (- 0 im)) (exp im)))
164.0ms
(cbrt (+ (exp (- im)) (exp im)))

simplify5.5s

Counts
45 → 86
Calls

45 calls. Slowest were:

504.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im)))) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im))))) (* (cbrt (+ (exp (- 0 im)) (exp im))) (cbrt (+ (exp (- 0 im)) (exp im))))))
496.0ms
(cbrt (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
426.0ms
(cbrt (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.5s

Algorithm
intervals