Average Error: 0.0 → 0.0
Time: 12.4s
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 2019022 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 12.0s)Debug log

sample83.0ms

Algorithm
intervals
Results
31.0ms49×body1280valid
22.0ms240×body80valid
15.0ms32×body640valid
5.0ms15×body320valid
1.0ms6×body160valid

simplify2.0ms

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

prune21.0ms

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
(* (exp re) (cos im))

rewrite5.0ms

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

series40.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
40.0ms
(* (exp re) (cos im))

simplify449.0ms

Counts
11 → 22
Calls
11 calls:
Slowest
386.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
46.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
4.0ms
(* (cos im) (exp re))
3.0ms
(* (cos im) (exp re))
2.0ms
(+ re (log (cos im)))

prune185.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
0.2b
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
0.1b
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
0.0b
(* (exp re) (cos im))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
140×pow1
67×pow-prod-down
59×add-cbrt-cube
41×add-exp-log
40×cbrt-unprod
40×prod-exp
30×pow-prod-up
15×pow-plus
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
5×associate-*l*
5×associate-*r*
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
4×pow2
3×*-commutative
2×pow3
1×rem-cbrt-cube
1×pow1/3
1×cbrt-prod
Counts
4 → 126
Calls
4 calls:
Slowest
46.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
40.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
21.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
4.0ms
(* (exp re) (cos im))

series193.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
58.0ms
(* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im)))
49.0ms
(* (exp re) (cos im))
46.0ms
(* (* (exp re) (cos im)) (* (exp re) (cos im)))
39.0ms
(cbrt (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))

simplify6.1s

Counts
114 → 138
Calls
114 calls:
Slowest
683.0ms
(* (* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))))
557.0ms
(* (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
537.0ms
(* (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))
504.0ms
(* (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))) (* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im))))
461.0ms
(* (* (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (* (exp re) (cos im)) (* (exp re) (cos im)))) (* (* (exp re) (cos im)) (* (exp re) (cos im)))) (* (* (* (exp re) (cos im)) (* (exp re) (cos im))) (* (exp re) (cos im))))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes181.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s1481×body1280valid
980.0ms6923×body80valid
631.0ms1294×body640valid
240.0ms609×body320valid
56.0ms304×body160valid