Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(\sin re \cdot 0.5\right) + e^{-im} \cdot \left(\sin re \cdot 0.5\right)\]

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019022 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 14.8s)Debug log

sample219.0ms

Algorithm
intervals
Results
106.0ms96×body1280valid
39.0ms65×body640valid
33.0ms246×body80valid
17.0ms41×body320valid
7.0ms25×body160valid

simplify289.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
289.0ms
(* (* 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

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-*r*
4×*-un-lft-identity
3×add-exp-log
3×add-cbrt-cube
3×pow1
2×add-cube-cbrt
2×associate-*r/
2×add-sqr-sqrt
1×add-log-exp
1×distribute-lft-out
1×flip-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×flip3-+
1×distribute-lft-in
1×distribute-rgt-in
Counts
1 → 20
Calls
1 calls:
Slowest
13.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series119.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
119.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify1.5s

Counts
14 → 23
Calls
14 calls:
Slowest
311.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
283.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
260.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
193.0ms
(* (* (* (* 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))))
191.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))

prune244.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*l*
7×add-cbrt-cube
7×pow1
5×add-log-exp
5×add-cube-cbrt
5×add-exp-log
5×*-un-lft-identity
5×add-sqr-sqrt
2×cbrt-unprod
2×*-commutative
2×prod-exp
2×associate-*l/
2×pow-prod-down
2×exp-sum
2×associate-*r*
1×sub0-neg
1×flip-+
1×exp-diff
1×distribute-rgt-out
1×flip3-+
1×sub-neg
1×sum-log
1×+-commutative
1×exp-neg
Counts
3 → 46
Calls
3 calls:
Slowest
10.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
9.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
4.0ms
(* (exp im) (* 0.5 (sin re)))

series256.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
116.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
79.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
61.0ms
(* (exp im) (* 0.5 (sin re)))

simplify2.6s

Counts
28 → 55
Calls
28 calls:
Slowest
480.0ms
(* (exp (* (exp (- 0 im)) (* 0.5 (sin re)))) (exp (* (exp im) (* 0.5 (sin re)))))
360.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
274.0ms
(* (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
267.0ms
(+ (* 0.5 (* (exp (- im)) (sin re))) (* 0.5 (* (sin re) (exp im))))
247.0ms
(- (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))) (* 0.5 (* re im)))

prune607.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes242.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.7s3025×body1280valid
2.2s2449×body640valid
1.7s8511×body80valid
593.0ms1199×body320valid
161.0ms596×body160valid