Average Error: 0.0 → 0.0
Time: 30.9s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2019002 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 30.4s)Debug log

sample266.0ms

Algorithm
intervals

simplify357.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

357.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
0.0b
(+ (exp (- 0 im)) (exp im))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

18.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
12.0ms
(+ (exp (- 0 im)) (exp im))

series121.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

96.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
25.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.9s

Counts
19 → 38
Calls

19 calls. Slowest were:

597.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
325.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
295.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))

prune416.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.5b
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

19.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))
8.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
7.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

series864.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

257.0ms
(* (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))) (cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))))
244.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
182.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
181.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

simplify10.1s

Counts
49 → 77
Calls

49 calls. Slowest were:

794.0ms
(* (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))) (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
708.0ms
(* (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))) (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
473.0ms
(- (+ (* 1/3 (* (pow (cbrt 0.5) 2) (* (pow im 2) (exp (* 1/3 (+ (log 4) (* 2 (log re)))))))) (* (pow (cbrt 0.5) 2) (exp (* 1/3 (+ (log 4) (* 2 (log re))))))) (* 1/9 (* (pow re 2) (* (pow (cbrt 0.5) 2) (exp (* 1/3 (+ (log 4) (* 2 (log re)))))))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

6.9b
(+ (* (exp im) (exp im)) -1)
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
0.6b
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 44
Calls

4 calls. Slowest were:

15.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))
6.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
6.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

series718.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

276.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (exp (- 0 im)) 3) (pow (exp im) 3))))
230.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
187.0ms
(cbrt (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))
25.0ms
(+ (* (exp im) (exp im)) -1)

simplify3.6s

Counts
22 → 56
Calls

22 calls. Slowest were:

441.0ms
(cbrt (* (* 0.5 (sin re)) (+ (pow (pow (exp (- 0 im)) 3) 3) (pow (pow (exp im) 3) 3))))
325.0ms
(- (+ (* (cbrt 0.5) (exp (* 1/3 (+ (log 2) (log re))))) (* 3/2 (* (cbrt 0.5) (* (pow im 2) (exp (* 1/3 (+ (log 2) (log re)))))))) (* 1/18 (* (pow re 2) (* (cbrt 0.5) (exp (* 1/3 (+ (log 2) (log re))))))))
305.0ms
(- (+ (* (cbrt 0.5) (exp (* 1/3 (+ (log 2) (log re))))) (* 1/6 (* (cbrt 0.5) (* (pow im 2) (exp (* 1/3 (+ (log 2) (log re)))))))) (* 1/18 (* (pow re 2) (* (cbrt 0.5) (exp (* 1/3 (+ (log 2) (log re))))))))

prune1.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes316.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample9.0s

Algorithm
intervals