Details

Time bar (total: 10.6s)

sample88.0ms

Algorithm
intervals
Results
36.0ms99×body1280valid
19.0ms77×body640valid
13.0ms290×body80valid
5.0ms38×body320valid
2.0ms18×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01011
12311
25611
38211
418411
525011
632211
756111
867811
971411
1084111
1186011
done86011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
4×associate-*r* add-log-exp
3×add-sqr-sqrt add-cube-cbrt pow-prod-down prod-exp cbrt-unprod
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×+-commutative distribute-rgt-in distribute-lft-in associate-*l* sum-log *-commutative
Counts
2 → 35
Calls
2 calls:
9.0ms
(+ (exp (- im)) (exp im))
27.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

series85.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(+ (exp (- im)) (exp im))
62.0ms
(* (* 0.5 (cos re)) (+ (exp (- im)) (exp im)))

simplify2.7s

Counts
41 → 41
Iterations

Useful iterations: 3 (907.0ms)

IterNodesCost
087548
1247530
2927441
34087437
done5000437

prune98.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube
9×add-exp-log
8×pow1
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×add-log-exp
4×prod-exp cbrt-unprod
3×times-frac associate-*l* pow-prod-down associate-/r*
2×cbrt-undiv div-exp
1×+-commutative frac-2neg flip3-+ associate-*r* clear-num sum-log *-commutative flip-+ div-inv associate-/l*
Counts
3 → 50
Calls
3 calls:
6.0ms
(/ (* 0.5 (cos re)) (exp im))
9.0ms
(+ (/ (* 0.5 (cos re)) (exp im)) (* (exp im) (* 0.5 (cos re))))
9.0ms
(* (exp im) (* 0.5 (cos re)))

series161.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ (* 0.5 (cos re)) (exp im))
82.0ms
(+ (/ (* 0.5 (cos re)) (exp im)) (* (exp im) (* 0.5 (cos re))))
42.0ms
(* (exp im) (* 0.5 (cos re)))

simplify706.0ms

Counts
59 → 59
Iterations

Useful iterations: done (704.0ms)

IterNodesCost
0102789
1278713
21080626
done5001606

prune130.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (exp im))
0.0b
(* (sqrt (exp im)) (* 0.5 (cos re)))
0.0b
(+ (/ (* 0.5 (cos re)) (exp im)) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
0.0b
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
18×add-exp-log add-cbrt-cube
12×associate-*l*
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down prod-exp sqrt-prod cbrt-unprod
6×add-log-exp
4×sqrt-pow1
3×exp-prod
2×associate-*r* *-commutative
1×+-commutative rem-sqrt-square flip3-+ pow1/2 sum-log flip-+
Counts
4 → 72
Calls
4 calls:
1.0ms
(sqrt (exp im))
13.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
11.0ms
(+ (/ (* 0.5 (cos re)) (exp im)) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
31.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(sqrt (exp im))
51.0ms
(* (sqrt (exp im)) (* 0.5 (cos re)))
81.0ms
(+ (/ (* 0.5 (cos re)) (exp im)) (* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re)))))
42.0ms
(* (sqrt (exp im)) (* (sqrt (exp im)) (* 0.5 (cos re))))

simplify551.0ms

Counts
84 → 84
Iterations

Useful iterations: done (549.0ms)

IterNodesCost
01221214
1312936
21073795
done5001766

prune182.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp im) (exp (- im)))
0.0b
(* (cos re) (+ (exp im) (exp (- im))))
0.3b
(pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3)
0.5b
(cbrt (pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
10×add-sqr-sqrt associate-*r/
8×cbrt-prod add-cube-cbrt
6×add-log-exp
4×cube-div flip3-+ associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
3×pow-unpow pow-pow associate-*l* pow-exp rem-cube-cbrt
2×cube-mult unpow-prod-down cbrt-div unpow3 cube-prod distribute-lft-out sqr-pow
1×+-commutative distribute-rgt-in pow-to-exp distribute-lft-in pow1/3 sum-log *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 81
Calls
4 calls:
5.0ms
(+ (exp im) (exp (- im)))
20.0ms
(* (cos re) (+ (exp im) (exp (- im))))
22.0ms
(pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3)
3.0ms
(cbrt (pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3))

series222.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (exp im) (exp (- im)))
48.0ms
(* (cos re) (+ (exp im) (exp (- im))))
90.0ms
(pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3)
61.0ms
(cbrt (pow (* 0.5 (* (cos re) (+ (exp im) (exp (- im))))) 3))

simplify545.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (145.0ms)

IterNodesCost
01431423
13641207
213221113
done50001113

prune249.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
11520
done1520

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s3006×body1280valid
551.0ms2570×body640valid
390.0ms8549×body80valid
183.0ms1264×body320valid
57.0ms590×body160valid