Average Error: 0.0 → 0.0
Time: 7.6s
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 2019022 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 7.2s)Debug log

sample114.0ms

Algorithm
intervals
Results
44.0ms49×body1280valid
32.0ms240×body80valid
19.0ms32×body640valid
6.0ms15×body320valid
2.0ms6×body160valid

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(* (exp re) (sin im))

prune19.0ms

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))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×add-exp-log
1×add-log-exp
1×log1p-expm1-u
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×expm1-log1p-u
Counts
1 → 19
Calls
1 calls:
Slowest
7.0ms
(* (exp re) (sin im))

series64.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
64.0ms
(* (exp re) (sin im))

simplify399.0ms

Counts
11 → 22
Calls
11 calls:
Slowest
306.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
75.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
3.0ms
(* (exp re) (sin im))
3.0ms
(+ re (log (sin im)))
2.0ms
(* (sin im) (exp re))

prune185.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 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))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sqrt-prod
12×associate-*l*
11×add-cube-cbrt
11×add-exp-log
11×add-cbrt-cube
11×*-un-lft-identity
11×pow1
4×add-log-exp
4×log1p-expm1-u
4×cbrt-unprod
4×prod-exp
4×pow-prod-down
4×associate-*r*
4×expm1-log1p-u
2×*-commutative
2×pow1/2
2×rem-sqrt-square
Counts
4 → 73
Calls
4 calls:
Slowest
18.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
4.0ms
(* (sqrt (exp re)) (sin im))
1.0ms
(sqrt (exp re))
1.0ms
(sqrt (exp re))

series154.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(* (sqrt (exp re)) (sin im))
63.0ms
(* (sqrt (exp re)) (* (sqrt (exp re)) (sin im)))
14.0ms
(sqrt (exp re))
11.0ms
(sqrt (exp re))

simplify1.6s

Counts
43 → 85
Calls
43 calls:
Slowest
472.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sin im)) (* (sqrt (exp re)) (sin im))) (* (sqrt (exp re)) (sin im))))
328.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
291.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im))))
246.0ms
(+ (* 1/8 (* (pow re 2) im)) (+ (* 1/2 (* re im)) im))
84.0ms
(* (* (* (sqrt (exp re)) (sqrt (exp re))) (sqrt (exp re))) (* (* (sin im) (sin im)) (sin im)))

prune734.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes165.0ms

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
Results
1.2s1290×body640valid
1.1s1483×body1280valid
834.0ms6924×body80valid
270.0ms612×body320valid
65.0ms301×body160valid