Average Error: 0.0 → 0.0
Time: 21.8s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot e^{\log \left(e^{im} + e^{-im}\right)}\right) \cdot 0.5\]

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. Using strategy rm

  3. Applied add-exp-log0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{e^{\log \left(e^{0 - im} + e^{im}\right)}}\]
  4. Using strategy rm

  5. Applied associate-*l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 21.1s)Debug log

sample348.0ms

Algorithm
intervals

simplify375.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

375.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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))

rewrite41.0ms

Algorithm
rewrite-expression-head
Counts
2 → 32
Calls

2 calls. Slowest were:

28.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
11.0ms
(+ (exp (- 0 im)) (exp im))

series510.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

485.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
25.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.7s

Counts
19 → 38
Calls

19 calls. Slowest were:

345.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
316.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
259.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))

prune458.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Counts
3 → 48
Calls

3 calls. Slowest were:

33.0ms
(* (* 0.5 (sin re)) (exp (log (+ (exp (- 0 im)) (exp im)))))
11.0ms
(+ (exp (- 0 im)) (exp im))
8.0ms
(log (+ (exp (- 0 im)) (exp im)))

series204.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

98.0ms
(log (+ (exp (- 0 im)) (exp im)))
79.0ms
(* (* 0.5 (sin re)) (exp (log (+ (exp (- 0 im)) (exp im)))))
27.0ms
(+ (exp (- 0 im)) (exp im))

simplify2.3s

Counts
30 → 57
Calls

30 calls. Slowest were:

386.0ms
(log (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
347.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
339.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))

prune711.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
3 → 50
Calls

3 calls. Slowest were:

21.0ms
(* (sin re) (exp (log (+ (exp (- 0 im)) (exp im)))))
6.0ms
(+ (exp (- 0 im)) (exp im))
4.0ms
(log (+ (exp (- 0 im)) (exp im)))

series218.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

103.0ms
(log (+ (exp (- 0 im)) (exp im)))
91.0ms
(* (sin re) (exp (log (+ (exp (- 0 im)) (exp im)))))
23.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.8s

Counts
32 → 59
Calls

32 calls. Slowest were:

446.0ms
(* (* (* (sin re) (sin re)) (sin re)) (* (* (exp (log (+ (exp (- 0 im)) (exp im)))) (exp (log (+ (exp (- 0 im)) (exp im))))) (exp (log (+ (exp (- 0 im)) (exp im))))))
368.0ms
(log (- (* (exp (- 0 im)) (exp (- 0 im))) (* (exp im) (exp im))))
260.0ms
(exp (log (+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))))

prune746.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
3 → 56
Calls

3 calls. Slowest were:

16.0ms
(+ (/ (sin re) (exp im)) (* (sin re) (exp im)))
7.0ms
(* (sin re) (exp im))
6.0ms
(/ (sin re) (exp im))

series227.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

120.0ms
(+ (/ (sin re) (exp im)) (* (sin re) (exp im)))
53.0ms
(* (sin re) (exp im))
53.0ms
(/ (sin re) (exp im))

simplify779.0ms

Counts
45 → 65
Calls

45 calls. Slowest were:

158.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))
134.0ms
(- (+ re (* re im)) (* 1/6 (pow re 3)))
132.0ms
(/ (* (* (sin re) (sin re)) (sin re)) (* (* (exp im) (exp im)) (exp im)))

prune715.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes272.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample9.4s

Algorithm
intervals