Details

Time bar (total: 25.9s)

sample276.0ms

Algorithm
intervals
Results
150.0ms182×body1280valid
64.0ms134×body640valid
13.0ms156×body80valid
13.0ms39×body320valid
4.0ms18×body160valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01112
12112
24412
310412
421212
570812
6468612
done500012

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
4.8b
(- (exp (- 0.0 im)) (exp im))

rewrite410.0ms

Algorithm
rewrite-expression-head
Rules
216×prod-diff
119×add-sqr-sqrt *-un-lft-identity
115×add-cube-cbrt
110×exp-sum
44×distribute-rgt-in distribute-lft-in
14×fma-neg
13×sub-neg
7×pow1 add-exp-log add-cbrt-cube
5×associate-*r*
4×add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
1×diff-log associate-*l* *-commutative
Counts
2 → 184
Calls
2 calls:
267.0ms
(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
120.0ms
(- (exp (- 0.0 im)) (exp im))

series165.0ms

Counts
2 → 6
Calls
2 calls:
106.0ms
(* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))
58.0ms
(- (exp (- 0.0 im)) (exp im))

simplify2.5s

Counts
190 → 190
Iterations

Useful iterations: 2 (574.0ms)

IterNodesCost
02847174
17864981
246223592
done50003592

prune422.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r*
6×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×distribute-lft-neg-in distribute-rgt-neg-in pow-prod-down prod-exp cbrt-unprod
2×distribute-neg-in fma-udef
1×distribute-rgt-in expm1-log1p-u neg-mul-1 distribute-lft-in associate-*l* *-commutative distribute-rgt-neg-out log1p-expm1-u add-log-exp
Counts
1 → 30
Calls
1 calls:
35.0ms
(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

series225.0ms

Counts
1 → 3
Calls
1 calls:
225.0ms
(* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))

simplify1.0s

Counts
33 → 33
Iterations

Useful iterations: done (1.0s)

IterNodesCost
092780
1274759
21472655
done5001642

prune226.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* -1/3 (pow im 3)) (* 0.5 (cos re)))
0.1b
(* (- (fma 1/60 (pow im 5) (* 2 im))) (* 0.5 (cos re)))
0.1b
(* -1/3 (pow im 3))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log
24×prod-exp
22×add-cbrt-cube
17×add-sqr-sqrt
14×associate-*r* associate-*l*
13×pow1
12×cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
6×pow-prod-down
4×unpow-prod-down cube-prod unswap-sqr
3×distribute-lft-neg-in expm1-log1p-u pow-to-exp distribute-rgt-neg-in pow-exp *-commutative log1p-expm1-u add-log-exp
2×sqr-pow
1×distribute-lft-neg-out cube-mult neg-mul-1 unpow3
Counts
3 → 87
Calls
3 calls:
58.0ms
(* (* -1/3 (pow im 3)) (* 0.5 (cos re)))
30.0ms
(* (- (fma 1/60 (pow im 5) (* 2 im))) (* 0.5 (cos re)))
29.0ms
(* -1/3 (pow im 3))

series242.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(* (* -1/3 (pow im 3)) (* 0.5 (cos re)))
105.0ms
(* (- (fma 1/60 (pow im 5) (* 2 im))) (* 0.5 (cos re)))
48.0ms
(* -1/3 (pow im 3))

simplify1.1s

Counts
96 → 96
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
01441221
13841121
21617963
done5000963

prune470.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))) (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))))
0.7b
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
0.7b
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
0.7b
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
77.0ms
(* (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))) (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))))
28.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
17.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
40.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
880.0ms
(* (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))) (cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im)))))))
469.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
441.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))
465.0ms
(cbrt (* (* 0.5 (cos re)) (- (fma 1/3 (pow im 3) (fma 1/60 (pow im 5) (* 2 im))))))

simplify978.0ms

Counts
78 → 78
Iterations

Useful iterations: done (973.0ms)

IterNodesCost
01562776
13932567
216382277
done50001939

prune717.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes461.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
12725
23125
33825
done3825

end0.0ms

sample9.9s

Algorithm
intervals
Results
5.5s5605×body1280valid
2.2s3582×body640valid
773.0ms1493×body320valid
498.0ms4214×body80valid
182.0ms696×body160valid