Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\sin im \cdot e^{re}\]

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

    \[e^{re} \cdot \sin im\]

  2. Final simplification0.0

    \[\leadsto \sin im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 6.9s)Debug log

sample71.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

2.0ms
(* (exp re) (sin im))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

4.0ms
(* (exp re) (sin im))

series61.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

61.0ms
(* (exp re) (sin im))

simplify385.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

292.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
73.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
5.0ms
(* (sin im) (exp re))

prune236.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (* (exp re) (sin im)))
0.3b
(sqrt (* (exp re) (sin im)))
0.2b
(* (sqrt (* (exp re) (sin im))) (sqrt (* (exp re) (sin im))))
0.0b
(* (exp re) (sin im))

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

12.0ms
(* (sqrt (* (exp re) (sin im))) (sqrt (* (exp re) (sin im))))
4.0ms
(sqrt (* (exp re) (sin im)))
4.0ms
(sqrt (* (exp re) (sin im)))

series242.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

67.0ms
(* (sqrt (* (exp re) (sin im))) (sqrt (* (exp re) (sin im))))
67.0ms
(sqrt (* (exp re) (sin im)))
56.0ms
(* (exp re) (sin im))
51.0ms
(sqrt (* (exp re) (sin im)))

simplify927.0ms

Counts
41 → 81
Calls

41 calls. Slowest were:

392.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
285.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
107.0ms
(* (* (* (sqrt (* (exp re) (sin im))) (sqrt (* (exp re) (sin im)))) (sqrt (* (exp re) (sin im)))) (* (* (sqrt (* (exp re) (sin im))) (sqrt (* (exp re) (sin im)))) (sqrt (* (exp re) (sin im)))))

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals