Average Error: 0.0 → 0.0
Time: 5.2s
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 2019018 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))

Details

Time bar (total: 4.8s)Debug log

sample99.0ms

Algorithm
intervals
Results
29.0ms34×body1280valid
24.0ms221×body80valid
20.0ms36×body640valid
9.0ms22×body320valid
3.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (cos im))

prune9.0ms

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))

rewrite4.0ms

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×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
Counts
1 → 17
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (cos im))

series51.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
51.0ms
(* (exp re) (cos im))

simplify89.0ms

Counts
11 → 20
Calls
11 calls:
Slowest
55.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (cos im) (cos im)) (cos im)))
23.0ms
(+ re (+ (* 1/2 (pow re 2)) 1))
2.0ms
(* (cos im) (exp re))
2.0ms
(* (exp re) (cos im))
2.0ms
(* (cos im) (exp re))

prune206.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(pow (* (cos im) (exp re)) 3)
0.2b
(cbrt (pow (* (cos im) (exp re)) 3))
0.0b
(* (cos im) (exp re))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-cbrt-cube
8×pow1
7×cbrt-prod
6×add-cube-cbrt
6×add-exp-log
6×*-un-lft-identity
6×add-sqr-sqrt
3×add-log-exp
3×associate-*l*
3×associate-*r*
2×rem-cube-cbrt
2×cbrt-unprod
2×prod-exp
2×pow-exp
2×pow-prod-down
2×cube-prod
2×unpow3
2×pow-pow
2×unpow-prod-down
2×cube-mult
1×rem-cbrt-cube
1×*-commutative
1×pow1/3
1×pow-to-exp
Counts
3 → 51
Calls
3 calls:
Slowest
7.0ms
(* (cos im) (exp re))
6.0ms
(pow (* (cos im) (exp re)) 3)
3.0ms
(cbrt (pow (* (cos im) (exp re)) 3))

series144.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
65.0ms
(pow (* (cos im) (exp re)) 3)
44.0ms
(cbrt (pow (* (cos im) (exp re)) 3))
35.0ms
(* (cos im) (exp re))

simplify399.0ms

Counts
33 → 60
Calls
33 calls:
Slowest
62.0ms
(- (+ (* 3 re) 1) (* 3/2 (pow im 2)))
47.0ms
(* (* (* (cos im) (cos im)) (cos im)) (* (* (exp re) (exp re)) (exp re)))
43.0ms
(- (+ re 1) (* 1/2 (pow im 2)))
40.0ms
(cbrt (sqrt (pow (* (cos im) (exp re)) 3)))
34.0ms
(* (pow (cos im) 3) (pow (exp re) 3))

prune593.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1492×body1280valid
949.0ms1206×body640valid
585.0ms6966×body80valid
236.0ms625×body320valid
82.0ms297×body160valid