Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]

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

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

  2. Final simplification0.0

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

Reproduce

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

Details

Time bar (total: 7.7s)Debug log

sample131.0ms

Algorithm
intervals

simplify4.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

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

series46.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

46.0ms
(* (exp re) (cos im))

simplify94.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

54.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
28.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
2.0ms
(* (cos im) (exp re))

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b
(log (exp (* (exp re) (cos im))))
0.1b
(exp (* (exp re) (cos im)))
0.0b
(* (exp re) (cos im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 47
Calls

3 calls. Slowest were:

4.0ms
(exp (* (exp re) (cos im)))
4.0ms
(* (exp re) (cos im))
4.0ms
(log (exp (* (exp re) (cos im))))

series172.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

83.0ms
(exp (* (exp re) (cos im)))
56.0ms
(* (exp re) (cos im))
33.0ms
(log (exp (* (exp re) (cos im))))

simplify309.0ms

Counts
26 → 56
Calls

26 calls. Slowest were:

129.0ms
(+ (* (pow re 2) E) (+ (* re E) E))
60.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
43.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))

prune664.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos im))
0.3b
(cbrt (cos im))
0.3b
(cbrt (cos im))
0.3b
(* (cbrt (cos im)) (cbrt (cos im)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (cos im)) (cbrt (cos im)))
1.0ms
(cbrt (cos im))
1.0ms
(cbrt (cos im))

series678.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

211.0ms
(* (cbrt (cos im)) (cbrt (cos im)))
169.0ms
(cbrt (cos im))
154.0ms
(cbrt (cos im))
145.0ms
(cbrt (cos im))

simplify525.0ms

Counts
41 → 81
Calls

41 calls. Slowest were:

143.0ms
(- 1 (+ (* 1/3 (pow im 2)) (* 1/405 (pow im 6))))
130.0ms
(- 1 (+ (* 1/6 (pow im 2)) (* 1/72 (pow im 4))))
103.0ms
(- 1 (+ (* 1/6 (pow im 2)) (* 1/72 (pow im 4))))

prune858.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes178.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.7s

Algorithm
intervals