Average Error: 0.0 → 0.0
Time: 18.0s
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 +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: 17.5s)Debug log

sample246.0ms

Algorithm
intervals
Results
103.0ms96×body1280valid
53.0ms246×body80valid
47.0ms65×body640valid
19.0ms41×body320valid
7.0ms25×body160valid

simplify476.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
476.0ms
(* (* 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

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

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×log1p-expm1-u
1×flip-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×flip3-+
1×distribute-lft-in
1×expm1-log1p-u
1×distribute-rgt-in
Counts
1 → 22
Calls
1 calls:
Slowest
15.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

series127.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
127.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

simplify2.2s

Counts
14 → 25
Calls
14 calls:
Slowest
473.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
426.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
416.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
304.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))
292.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))

prune312.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

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))))

rewrite26.0ms

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
3×log1p-expm1-u
3×expm1-log1p-u
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×fma-def
1×sub-neg
1×sum-log
1×+-commutative
1×exp-neg
Counts
3 → 53
Calls
3 calls:
Slowest
12.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
8.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
5.0ms
(* (exp im) (* 0.5 (sin re)))

series264.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
128.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
75.0ms
(* (exp im) (* 0.5 (sin re)))
61.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))

simplify4.1s

Counts
29 → 62
Calls
29 calls:
Slowest
1.1s
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
538.0ms
(* (exp (* (exp (- 0 im)) (* 0.5 (sin re)))) (exp (* (exp im) (* 0.5 (sin re)))))
459.0ms
(+ (* 0.5 (* re im)) (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))))
410.0ms
(+ (* 0.5 (* (exp (- im)) (sin re))) (* 0.5 (* (sin re) (exp im))))
372.0ms
(- (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))) (* 0.5 (* re im)))

prune617.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes192.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.3s3025×body1280valid
2.4s2449×body640valid
2.0s8511×body80valid
625.0ms1199×body320valid
178.0ms596×body160valid