Average Error: 0.0 → 0.0
Time: 45.6s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{0.5 \cdot \sin re}{e^{im}}\]

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

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

  5. Applied sub0-neg0.0

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

  6. Applied exp-neg0.0

    \[\leadsto \color{blue}{\frac{1}{e^{im}}} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]

  7. Applied associate-*l/0.0

    \[\leadsto \color{blue}{\frac{1 \cdot \left(0.5 \cdot \sin re\right)}{e^{im}}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019018 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))

Details

Time bar (total: 44.8s)Debug log

sample218.0ms

Algorithm
intervals
Results
75.0ms77×body1280valid
39.0ms59×body640valid
36.0ms273×body80valid
23.0ms22×body160valid
19.0ms44×body320valid

simplify311.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
311.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

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))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
4×add-log-exp
4×add-exp-log
4×associate-*r*
4×add-cbrt-cube
4×pow1
3×add-cube-cbrt
3×add-sqr-sqrt
2×distribute-lft-out
2×flip-+
2×associate-*r/
2×flip3-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×distribute-lft-in
1×sum-log
1×+-commutative
1×distribute-rgt-in
Counts
2 → 32
Calls
2 calls:
Slowest
27.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
11.0ms
(+ (exp (- 0 im)) (exp im))

series125.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
42.0ms
(+ (exp (- 0 im)) (exp im))

simplify1.4s

Counts
19 → 38
Calls
19 calls:
Slowest
313.0ms
(* 0.5 (* (sin re) (+ (exp im) (exp (* -1 im)))))
257.0ms
(* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im)))
242.0ms
(* 0.5 (* (sin re) (+ (exp (- im)) (exp im))))
198.0ms
(+ (* (exp (- 0 im)) (exp (- 0 im))) (- (* (exp im) (exp im)) (* (exp (- 0 im)) (exp im))))
124.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))

prune464.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

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
21.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
15.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
10.0ms
(* (exp im) (* 0.5 (sin re)))

series293.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
154.0ms
(+ (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))
79.0ms
(* (exp (- 0 im)) (* 0.5 (sin re)))
59.0ms
(* (exp im) (* 0.5 (sin re)))

simplify2.6s

Counts
28 → 55
Calls
28 calls:
Slowest
454.0ms
(* (exp (* (exp (- 0 im)) (* 0.5 (sin re)))) (exp (* (exp im) (* 0.5 (sin re)))))
355.0ms
(+ (* 0.5 (* (sin re) (exp (* -1 im)))) (* 0.5 (* (sin re) (exp im))))
275.0ms
(* (* (* (exp (- 0 im)) (exp (- 0 im))) (exp (- 0 im))) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
256.0ms
(- (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))) (* 0.5 (* re im)))
240.0ms
(+ (* 0.5 (* (exp (- im)) (sin re))) (* 0.5 (* (sin re) (exp im))))

prune672.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* 0.5 (sin re)) (exp im))
0.0b
(+ (/ (* 0.5 (sin re)) (exp im)) (* (exp im) (* 0.5 (sin re))))
0.0b
(* (exp im) (* 0.5 (sin re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×add-cbrt-cube
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
5×add-log-exp
5×add-exp-log
5×pow1
3×associate-*l*
3×times-frac
3×associate-/r*
1×associate-/l*
1×div-inv
1×flip-+
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×associate-*r*
1×div-exp
1×flip3-+
1×frac-2neg
1×sum-log
1×clear-num
1×+-commutative
1×cbrt-undiv
Counts
3 → 45
Calls
3 calls:
Slowest
9.0ms
(+ (/ (* 0.5 (sin re)) (exp im)) (* (exp im) (* 0.5 (sin re))))
7.0ms
(* (exp im) (* 0.5 (sin re)))
4.0ms
(/ (* 0.5 (sin re)) (exp im))

series264.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
140.0ms
(+ (/ (* 0.5 (sin re)) (exp im)) (* (exp im) (* 0.5 (sin re))))
69.0ms
(* (exp im) (* 0.5 (sin re)))
54.0ms
(/ (* 0.5 (sin re)) (exp im))

simplify1.9s

Counts
27 → 54
Calls
27 calls:
Slowest
583.0ms
(/ (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))) (* (* (exp im) (exp im)) (exp im)))
564.0ms
(+ (* 0.5 (* re im)) (+ (* 0.5 re) (* 0.25 (* re (pow im 2)))))
237.0ms
(* (* (* (exp im) (exp im)) (exp im)) (* (* (* 0.5 (sin re)) (* 0.5 (sin re))) (* 0.5 (sin re))))
165.0ms
(- (* 0.5 re) (+ (* 0.5 (* re im)) (* 0.08333333333333333 (pow re 3))))
157.0ms
(- (+ (* 1.0 re) (* 0.5 (* re (pow im 2)))) (* 0.16666666666666666 (pow re 3)))

prune598.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

22.5b
(/ (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3)) (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))))
4.7b
(- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))
0.4b
(pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3)
0.4b
(pow (* (exp im) (* 0.5 (sin re))) 3)

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
30×associate-*l/
27×times-frac
26×*-un-lft-identity
18×add-cube-cbrt
18×associate-/r/
18×cube-prod
18×unpow-prod-down
18×add-sqr-sqrt
16×frac-add
16×distribute-rgt-out
13×sub0-neg
13×exp-diff
13×exp-neg
12×add-cbrt-cube
10×add-exp-log
10×pow1
9×associate-/l*
9×flip--
9×flip3--
8×frac-times
6×add-log-exp
4×rem-cube-cbrt
4×distribute-lft-out
4×sum-cubes
4×associate-*r/
4×pow-exp
4×pow-pow
3×associate-/r*
2×associate-/l/
2×flip-+
2×cbrt-unprod
2×prod-exp
2×pow-prod-down
2×unpow3
2×flip3-+
2×pow-to-exp
2×cube-mult
2×cube-div
1×div-inv
1×div-exp
1×diff-log
1×distribute-rgt-out--
1×frac-2neg
1×sub-neg
1×clear-num
1×cbrt-undiv
Counts
4 → 122
Calls
4 calls:
Slowest
142.0ms
(/ (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3)) (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))))
40.0ms
(- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))
9.0ms
(pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3)
4.0ms
(pow (* (exp im) (* 0.5 (sin re))) 3)

series770.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
420.0ms
(/ (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3)) (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))))
191.0ms
(- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))
88.0ms
(pow (* (exp im) (* 0.5 (sin re))) 3)
70.0ms
(pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3)

simplify23.6s

Counts
119 → 134
Calls
119 calls:
Slowest
684.0ms
(/ (* (* (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3)) (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3))) (+ (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) (pow (* (exp im) (* 0.5 (sin re))) 3))) (* (* (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))))) (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))))) (+ (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp (- 0 im)) (* 0.5 (sin re)))) (- (* (* (exp im) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re)))) (* (* (exp (- 0 im)) (* 0.5 (sin re))) (* (exp im) (* 0.5 (sin re))))))))
650.0ms
(/ (pow (* 0.5 (sin re)) 3) 1)
593.0ms
(+ (pow (pow (* (exp (- 0 im)) (* 0.5 (sin re))) 3) 3) (pow (pow (* (exp im) (* 0.5 (sin re))) 3) 3))
590.0ms
(/ (pow (* 0.5 (sin re)) 3) 1)
574.0ms
(/ (pow (* 0.5 (sin re)) 3) 1)

prune2.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes144.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
4.1s2904×body1280valid
1.8s2418×body640valid
1.4s8533×body80valid
725.0ms1254×body320valid
191.0ms666×body160valid