Average Error: 0.0 → 0.0
Time: 16.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot (\left(\sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{e^{im}}\right))_*\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 3.7s)Debug log

start380.0ms

Algorithm
intervals

setup133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (sin re) (exp im))
0.0b
(fma (sin re) (exp im) (/ (sin re) (exp im)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 39
Calls

2 calls. Slowest were:

8.0ms
(/ (sin re) (exp im))
0.0ms
(fma (sin re) (exp im) (/ (sin re) (exp im)))

series161.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

88.0ms
(fma (sin re) (exp im) (/ (sin re) (exp im)))
73.0ms
(/ (sin re) (exp im))

simplify585.0ms

Counts
31 → 45
Calls

31 calls. Slowest were:

194.0ms
(- re (+ (* re im) (* 1/6 (pow re 3))))
163.0ms
(- (+ (* 2 re) (* re (pow im 2))) (* 1/3 (pow re 3)))
139.0ms
(/ (* (* (sin re) (sin re)) (sin re)) (* (* (exp im) (exp im)) (exp im)))

prune520.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Counts
1 → 22
Calls

1 calls. Slowest were:

26.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series93.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

93.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify1.1s

Counts
14 → 25
Calls

14 calls. Slowest were:

229.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))
174.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))
153.0ms
(* (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (+ (exp (- 0 im)) (exp im)) (+ (exp (- 0 im)) (exp im))) (+ (exp (- 0 im)) (exp im))))

prune331.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes256.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms