Average Error: 0.0 → 0.0
Time: 13.5s
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 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 13.2s)Debug log

sample132.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune10.0ms

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 → 17
Calls

1 calls. Slowest were:

7.0ms
(* (exp re) (sin im))

series47.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

47.0ms
(* (exp re) (sin im))

simplify199.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

95.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
87.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
4.0ms
(* (sin im) (exp re))

prune131.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

14.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
6.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))

series145.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(* (sqrt (exp re)) (sin im))
58.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
13.0ms
(sqrt (exp re))
12.0ms
(sqrt (exp re))

simplify1.2s

Counts
43 → 77
Calls

43 calls. Slowest were:

414.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
351.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
125.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune652.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

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)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

30.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))
11.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))

series324.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

140.0ms
(sqrt (sqrt (exp re)))
98.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
48.0ms
(* (sqrt (exp re)) (sin im))
38.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im))))

simplify2.4s

Counts
64 → 99
Calls

64 calls. Slowest were:

572.0ms
(* (* (* (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)))))
472.0ms
(* (* (* (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))))
323.0ms
(* (* (* (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))))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

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))

rewrite79.0ms

Algorithm
rewrite-expression-head
Counts
4 → 77
Calls

4 calls. Slowest were:

45.0ms
(* (sqrt (sqrt (exp re))) (* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im))))
22.0ms
(* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im)))
8.0ms
(* (sqrt (exp re)) (sin im))

series248.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

115.0ms
(* (sqrt (sqrt (exp re))) (* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im))))
74.0ms
(* (exp (* 1/4 re)) (* (sqrt (exp re)) (sin im)))
47.0ms
(* (sqrt (exp re)) (sin im))
11.0ms
(sqrt (exp re))

simplify1.6s

Counts
54 → 89
Calls

54 calls. Slowest were:

254.0ms
(* (* (* (exp (* 1/4 re)) (exp (* 1/4 re))) (exp (* 1/4 re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
214.0ms
(* (* (* (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))))
103.0ms
(* (* (* (sqrt (sqrt (exp re))) (sqrt (sqrt (exp re)))) (sqrt (sqrt (exp re)))) (* (* (* (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)))))

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes133.0ms

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