Average Error: 0.0 → 0.0
Time: 26.9s
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 2018365 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 13.2s)Debug log

start393.0ms

Algorithm
intervals

setup338.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
1 → 20
Calls

1 calls. Slowest were:

27.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series134.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

133.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify1.8s

Counts
14 → 23
Calls

14 calls. Slowest were:

372.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
369.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
318.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

19.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
13.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
9.0ms
(* (* 0.5 (sin re)) (exp im))

series212.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

109.0ms
(+ (* (* 0.5 (sin re)) (exp (- 0 im))) (* (* 0.5 (sin re)) (exp im)))
54.0ms
(* (* 0.5 (sin re)) (exp (- 0 im)))
49.0ms
(* (* 0.5 (sin re)) (exp im))

simplify2.7s

Counts
29 → 56
Calls

29 calls. Slowest were:

392.0ms
(* (exp (* (* 0.5 (sin re)) (exp (- 0 im)))) (exp (* (* 0.5 (sin re)) (exp im))))
389.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
298.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))))

prune734.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Counts
4 → 76
Calls

4 calls. Slowest were:

33.0ms
(* (* (* 0.5 (sin re)) (sqrt (exp (- 0 im)))) (sqrt (exp (- im))))
17.0ms
(+ (* (* (* 0.5 (sin re)) (sqrt (exp (- 0 im)))) (sqrt (exp (- im)))) (* (* 0.5 (sin re)) (exp im)))
6.0ms
(* (* 0.5 (sin re)) (sqrt (exp (- 0 im))))

series243.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

113.0ms
(+ (* (* (* 0.5 (sin re)) (sqrt (exp (- 0 im)))) (sqrt (exp (- im)))) (* (* 0.5 (sin re)) (exp im)))
65.0ms
(* (* 0.5 (sin re)) (sqrt (exp (- 0 im))))
51.0ms
(* (* (* 0.5 (sin re)) (sqrt (exp (- 0 im)))) (sqrt (exp (- im))))
14.0ms
(sqrt (exp (- im)))

simplify4.3s

Counts
57 → 88
Calls

57 calls. Slowest were:

803.0ms
(* (* (* (* (* 0.5 (sin re)) (sqrt (exp (- 0 im)))) (* (* 0.5 (sin re)) (sqrt (exp (- 0 im))))) (* (* 0.5 (sin re)) (sqrt (exp (- 0 im))))) (* (* (sqrt (exp (- im))) (sqrt (exp (- im)))) (sqrt (exp (- im)))))
710.0ms
(* (* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (sqrt (exp (- 0 im))) (sqrt (exp (- 0 im)))) (sqrt (exp (- 0 im))))) (* (* (sqrt (exp (- im))) (sqrt (exp (- im)))) (sqrt (exp (- im)))))
361.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes330.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms