Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[e^{re} \cdot \sin im\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 8.3s)Debug log

start164.0ms

Algorithm
intervals

setup10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 19
Calls

1 calls. Slowest were:

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

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(* (sin im) (exp re))

simplify404.0ms

Counts
11 → 22
Calls

11 calls. Slowest were:

341.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
51.0ms
(* (* (* (sin im) (sin im)) (sin im)) (* (* (exp re) (exp re)) (exp re)))
2.0ms
(* (sin im) (exp re))

prune199.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Counts
4 → 89
Calls

4 calls. Slowest were:

51.0ms
(* (* (sin im) (* (cbrt (exp re)) (cbrt (exp re)))) (cbrt (exp re)))
22.0ms
(* (sin im) (* (cbrt (exp re)) (cbrt (exp re))))
10.0ms
(* (cbrt (exp re)) (cbrt (exp re)))

series415.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

136.0ms
(* (cbrt (exp re)) (cbrt (exp re)))
132.0ms
(cbrt (exp re))
110.0ms
(* (sin im) (* (cbrt (exp re)) (cbrt (exp re))))
36.0ms
(* (* (sin im) (* (cbrt (exp re)) (cbrt (exp re)))) (cbrt (exp re)))

simplify1.8s

Counts
60 → 101
Calls

60 calls. Slowest were:

321.0ms
(- (+ (* 2/3 (* re im)) im) (* 1/6 (pow im 3)))
304.0ms
(- (+ (* re im) im) (* 1/6 (pow im 3)))
286.0ms
(* (* (* (* (sin im) (sin im)) (sin im)) (* (* (* (cbrt (exp re)) (cbrt (exp re))) (* (cbrt (exp re)) (cbrt (exp re)))) (* (cbrt (exp re)) (cbrt (exp re))))) (exp re))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sin im) (pow (* (exp re) (exp re)) 1/3))
0.0b
(* (* (sin im) (pow (* (exp re) (exp re)) 1/3)) (cbrt (exp re)))
0.0b
(* (exp re) (exp re))
0.0b
(pow (* (exp re) (exp re)) 1/3)

rewrite62.0ms

Algorithm
rewrite-expression-head
Counts
4 → 90
Calls

4 calls. Slowest were:

33.0ms
(* (* (sin im) (pow (* (exp re) (exp re)) 1/3)) (cbrt (exp re)))
14.0ms
(* (sin im) (pow (* (exp re) (exp re)) 1/3))
7.0ms
(* (exp re) (exp re))

series372.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

150.0ms
(pow (* (exp re) (exp re)) 1/3)
149.0ms
(* (sin im) (pow (* (exp re) (exp re)) 1/3))
56.0ms
(* (* (sin im) (pow (* (exp re) (exp re)) 1/3)) (cbrt (exp re)))
16.0ms
(* (exp re) (exp re))

simplify2.3s

Counts
59 → 102
Calls

59 calls. Slowest were:

338.0ms
(* (* (* (* (sin im) (pow (* (exp re) (exp re)) 1/3)) (* (sin im) (pow (* (exp re) (exp re)) 1/3))) (* (sin im) (pow (* (exp re) (exp re)) 1/3))) (exp re))
310.0ms
(* (* (* (* (sin im) (sin im)) (sin im)) (* (* (pow (* (exp re) (exp re)) 1/3) (pow (* (exp re) (exp re)) 1/3)) (pow (* (exp re) (exp re)) 1/3))) (exp re))
281.0ms
(- (+ (* 2/3 (* re im)) im) (* 1/6 (pow im 3)))

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms