Average Error: 0.0 → 0.0
Time: 15.9s
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 2019005 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 15.5s)Debug log

sample150.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

8.0ms
(* (exp re) (sin im))

series60.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

60.0ms
(* (exp re) (sin im))

simplify417.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

353.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
48.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
4.0ms
(* (exp re) (sin im))

prune147.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

11.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))

series123.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

50.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
48.0ms
(* (sqrt (exp re)) (sin im))
13.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.6s

Counts
43 → 85
Calls

43 calls. Slowest were:

459.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
363.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
327.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune912.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Counts
4 → 95
Calls

4 calls. Slowest were:

26.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))
18.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
8.0ms
(* (sqrt (exp re)) (sin im))

series323.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

127.0ms
(sqrt (sqrt (exp re)))
109.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
47.0ms
(* (sqrt (exp re)) (sin im))
40.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))

simplify2.5s

Counts
64 → 107
Calls

64 calls. Slowest were:

474.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))))
322.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
285.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (sqrt (exp re))) (* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im))))
0.0b
(* (sqrt (exp re)) (sin im))
0.0b
(* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im)))
0.0b
(sqrt (exp re))

rewrite45.0ms

Algorithm
rewrite-expression-head
Counts
4 → 85
Calls

4 calls. Slowest were:

27.0ms
(* (sqrt (sqrt (exp re))) (* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im))))
11.0ms
(* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im)))
5.0ms
(* (sqrt (exp re)) (sin im))

series319.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

139.0ms
(* (sqrt (sqrt (exp re))) (* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im))))
95.0ms
(* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im)))
73.0ms
(* (sqrt (exp re)) (sin im))
12.0ms
(sqrt (exp re))

simplify2.4s

Counts
54 → 97
Calls

54 calls. Slowest were:

357.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
305.0ms
(* (* (* (exp (* 1/4 re)) (exp (* 1/4 re))) (exp (* 1/4 re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
279.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes201.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm
intervals