Average Error: 0.0 → 0.0
Time: 8.6s
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 2018360 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 4.2s)Debug log

start111.0ms

Algorithm
intervals

setup11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series66.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

66.0ms
(* (exp re) (sin im))

simplify151.0ms

Counts
11 → 20
Calls

11 calls. Slowest were:

79.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
58.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
3.0ms
(* (sin im) (exp re))

prune195.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

10.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))

series167.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

80.0ms
(* (sqrt (exp re)) (sin im))
46.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
21.0ms
(sqrt (exp re))
20.0ms
(sqrt (exp re))

simplify1.2s

Counts
43 → 77
Calls

43 calls. Slowest were:

482.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
285.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
98.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune770.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (pow re 2) im)
4.0b
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
0.0b
(+ (* re im) im)
0.0b
(* 1/2 (* (pow re 2) im))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 44
Calls

4 calls. Slowest were:

9.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
6.0ms
(* 1/2 (* (pow re 2) im))
3.0ms
(+ (* re im) im)

series63.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

18.0ms
(* (pow re 2) im)
17.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
15.0ms
(* 1/2 (* (pow re 2) im))
13.0ms
(+ (* re im) im)

simplify509.0ms

Counts
16 → 56
Calls

16 calls. Slowest were:

126.0ms
(* (exp (* 1/2 (* (pow re 2) im))) (exp (+ (* re im) im)))
110.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
99.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))

prune619.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes210.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms