Average Error: 0.0 → 0.3
Time: 13.2s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \log \left(e^{\sqrt{e^{re}}}\right)\]

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

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)} \cdot \sin im\]

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)}\]
  5. Using strategy rm

  6. Applied add-log-exp0.3

    \[\leadsto \color{blue}{\log \left(e^{\sqrt{e^{re}}}\right)} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]

  7. Final simplification0.3

    \[\leadsto \left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \log \left(e^{\sqrt{e^{re}}}\right)\]

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 12.5s)Debug log

sample111.0ms

Algorithm
intervals

simplify6.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

6.0ms
(* (exp re) (sin im))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

series69.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

69.0ms
(* (exp re) (sin im))

simplify425.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

342.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
63.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
4.0ms
(* (exp re) (sin im))

prune198.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

20.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
5.0ms
(* (sqrt (exp re)) (sin im))
2.0ms
(sqrt (exp re))

series159.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

71.0ms
(* (sqrt (exp re)) (sin im))
51.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
19.0ms
(sqrt (exp re))
18.0ms
(sqrt (exp re))

simplify1.5s

Counts
43 → 85
Calls

43 calls. Slowest were:

398.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
358.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
294.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
4 → 71
Calls

4 calls. Slowest were:

20.0ms
(* (log (exp (sqrt (exp re)))) (* (sqrt (exp re)) (sin im)))
2.0ms
(exp (sqrt (exp re)))
1.0ms
(sqrt (exp re))

series173.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

89.0ms
(exp (sqrt (exp re)))
45.0ms
(* (log (exp (sqrt (exp re)))) (* (sqrt (exp re)) (sin im)))
20.0ms
(sqrt (exp re))
20.0ms
(sqrt (exp re))

simplify1.4s

Counts
42 → 83
Calls

42 calls. Slowest were:

365.0ms
(* (* (* (log (exp (sqrt (exp re)))) (log (exp (sqrt (exp re))))) (log (exp (sqrt (exp re))))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
353.0ms
(* (* (* (log (exp (sqrt (exp re)))) (log (exp (sqrt (exp re))))) (log (exp (sqrt (exp re))))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
305.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune968.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

12.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series175.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

113.0ms
(* (sqrt (sqrt (exp re))) (* (sqrt (exp re)) (sin im)))
21.0ms
(sqrt (exp re))
21.0ms
(sqrt (exp re))
20.0ms
(sqrt (exp re))

simplify1.2s

Counts
39 → 80
Calls

39 calls. Slowest were:

365.0ms
(* (* (* (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))))
329.0ms
(* (* (* (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))))
236.0ms
(+ (* 9/32 (* (pow re 2) im)) (+ (* 3/4 (* re im)) im))

prune924.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes311.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals