Average Error: 0.0 → 0.0
Time: 21.5s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \left(0.5 \cdot \cos re\right) \cdot e^{-im}\]

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

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

Details

Time bar (total: 21.1s)Debug log

sample302.0ms

Algorithm
intervals
Results
520×(pre true 80)
274×(body real 80)
107×(body real 1280)
70×(body real 640)
51×(body real 320)
18×(body real 160)

simplify613.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
613.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

rewrite18.0ms

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
18.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series61.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
61.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify1.6s

Counts
14 → 25
Calls
14 calls:
Slowest
462.0ms
(* 0.5 (* (cos re) (+ (exp (- im)) (exp im))))
288.0ms
(+ (* (exp (- im)) (exp (- im))) (- (* (exp im) (exp im)) (* (exp (- im)) (exp im))))
222.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))
208.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (+ (exp (- im)) (exp im)) (+ (exp (- im)) (exp im))) (+ (exp (- im)) (exp im))))
193.0ms
(* 0.5 (* (+ (exp im) (exp (* -1 im))) (cos re)))

prune274.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
0.0b
(* (* 0.5 (cos re)) (exp (- im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
4×add-cbrt-cube
4×pow1
3×add-cube-cbrt
3×add-exp-log
3×associate-*r*
3×*-un-lft-identity
3×add-sqr-sqrt
2×log1p-expm1-u
2×associate-*r/
2×expm1-log1p-u
2×exp-neg
1×distribute-lft-out
1×flip-+
1×cbrt-unprod
1×*-commutative
1×un-div-inv
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×exp-diff
1×flip3-+
1×fma-def
1×sum-log
1×+-commutative
1×neg-sub0
Counts
2 → 35
Calls
2 calls:
Slowest
11.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
7.0ms
(* (* 0.5 (cos re)) (exp (- im)))

series163.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
121.0ms
(+ (* (* 0.5 (cos re)) (exp (- im))) (* (* 0.5 (cos re)) (exp im)))
41.0ms
(* (* 0.5 (cos re)) (exp (- im)))

simplify1.9s

Counts
19 → 41
Calls
19 calls:
Slowest
512.0ms
(+ (* 0.5 (* (exp im) (cos re))) (* 0.5 (* (exp (* -1 im)) (cos re))))
371.0ms
(+ (* 0.5 (* (exp (- im)) (cos re))) (* 0.5 (* (exp im) (cos re))))
296.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (exp (- im)) (exp (- im))) (exp (- im))))
224.0ms
(* (exp (* (* 0.5 (cos re)) (exp (- im)))) (exp (* (* 0.5 (cos re)) (exp im))))
116.0ms
(- 0.5 (+ (* 0.25 (pow re 2)) (* 0.5 im)))

prune434.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (+ (exp (- im)) (exp im)))
1.0b
(cbrt (+ (exp (- im)) (exp im)))
1.0b
(cbrt (+ (exp (- im)) (exp im)))
0.2b
(* (* 0.5 (cos re)) (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×cbrt-prod
10×associate-*r/
9×flip-+
9×add-exp-log
9×flip3-+
9×pow1
7×add-cube-cbrt
7×add-cbrt-cube
7×add-sqr-sqrt
4×add-log-exp
4×log1p-expm1-u
4×frac-times
4×expm1-log1p-u
3×distribute-lft-out
3×cbrt-unprod
3×prod-exp
3×pow-prod-down
3×pow1/3
2×associate-*l/
1×*-commutative
1×associate-*l*
1×associate-*r*
Counts
4 → 74
Calls
4 calls:
Slowest
61.0ms
(* (* 0.5 (cos re)) (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im)))))
11.0ms
(cbrt (+ (exp (- im)) (exp im)))
8.0ms
(cbrt (+ (exp (- im)) (exp im)))
7.0ms
(cbrt (+ (exp (- im)) (exp im)))

series755.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
238.0ms
(cbrt (+ (exp (- im)) (exp im)))
200.0ms
(cbrt (+ (exp (- im)) (exp im)))
182.0ms
(cbrt (+ (exp (- im)) (exp im)))
134.0ms
(* (* 0.5 (cos re)) (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im)))))

simplify4.8s

Counts
45 → 86
Calls
45 calls:
Slowest
422.0ms
(* (* (* (* 0.5 (cos re)) (* 0.5 (cos re))) (* 0.5 (cos re))) (* (* (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im)))) (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im))))) (* (cbrt (+ (exp (- im)) (exp im))) (cbrt (+ (exp (- im)) (exp im))))))
364.0ms
(cbrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im))))
352.0ms
(cbrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im))))
331.0ms
(cbrt (- (* (exp (- im)) (exp (- im))) (* (exp im) (exp im))))
304.0ms
(- (+ (* 1/6 (* (pow im 2) (pow 2 1/3))) (pow 2 1/3)) (* 1/72 (* (pow im 4) (pow 2 1/3))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes139.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
15930×(pre true 80)
8580×(body real 80)
3042×(body real 1280)
2476×(body real 640)
1220×(body real 320)
612×(body real 160)