Details

Time bar (total: 9.2s)

sample28.0ms

Algorithm
intervals
Results
6.0ms184×body80valid
5.0ms27×body2560valid
3.0ms13×body5120valid
2.0ms15×body1280valid
2.0ms14×body640valid
0.0ms3×body320valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11715
22415
33015
43515
done3515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(- (sqrt (+ (* re re) (* im im))) re)
29.0b
(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×*-un-lft-identity
4×sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×add-exp-log sqrt-div add-cbrt-cube difference-of-squares
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ distribute-lft-out--
Counts
2 → 30
Calls
2 calls:
38.0ms
(- (sqrt (+ (* re re) (* im im))) re)
10.0ms
(sqrt (+ (* re re) (* im im)))

series97.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(- (sqrt (+ (* re re) (* im im))) re)
50.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts
36 → 36
Iterations

Useful iterations: 4 (602.0ms)

IterNodesCost
064481
1137421
2328391
3767381
41986379
done5000379

prune109.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.1b
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.0b
(sqrt (+ (* re re) (* im im)))
29.0b
(sqrt (+ (* re re) (* im im)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-+ flip-+
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 126
Calls
4 calls:
53.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
38.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))
10.0ms
(sqrt (+ (* re re) (* im im)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts
138 → 138
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01383069
12591761
26651607
319341548
done50001507

prune282.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ re (sqrt (+ (* re re) (* im im))))
7.5b
(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
18.7b
(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
29.0b
(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×pow1 add-sqr-sqrt
7×add-cube-cbrt
6×add-log-exp
4×times-frac associate-/r* sqrt-prod
3×sqrt-pow1 flip3-+ sqrt-div flip-+ distribute-lft-out
2×cbrt-undiv pow1/2 div-exp associate-/r/
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
4 → 64
Calls
4 calls:
14.0ms
(+ re (sqrt (+ (* re re) (* im im))))
23.0ms
(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
37.0ms
(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
8.0ms
(sqrt (+ (* re re) (* im im)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ re (sqrt (+ (* re re) (* im im))))
185.0ms
(sqrt (* 2.0 (/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))))
67.0ms
(/ (* im im) (+ re (sqrt (+ (* re re) (* im im)))))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
76 → 76
Iterations

Useful iterations: 3 (777.0ms)

IterNodesCost
01461254
13571132
210841009
33719979
done5000979

prune188.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
0.7b
(+ re (sqrt (+ (* re re) (* im im))))
7.5b
(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
29.0b
(sqrt (+ (* re re) (* im im)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
80×*-un-lft-identity
55×add-sqr-sqrt
54×add-cube-cbrt
16×associate-/r*
13×distribute-lft-out
9×add-exp-log add-cbrt-cube
8×pow1
6×add-log-exp
5×div-inv
4×sqrt-prod
3×cbrt-undiv sqrt-pow1 sqrt-div div-exp associate-/l*
2×flip3-+ pow1/2 flip-+
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log associate-/r/
Counts
4 → 121
Calls
4 calls:
34.0ms
(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
14.0ms
(+ re (sqrt (+ (* re re) (* im im))))
21.0ms
(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
9.0ms
(sqrt (+ (* re re) (* im im)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))
49.0ms
(+ re (sqrt (+ (* re re) (* im im))))
201.0ms
(sqrt (* 2.0 (/ im (/ (+ re (sqrt (+ (* re re) (* im im)))) im))))
34.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
133 → 133
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02442856
15562658
218262485
done50002445

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

regimes274.0ms

Accuracy

38.7% (22.0b remaining)

Error of 26.2b against oracle of 4.2b and baseline of 40.1b

bsearch421.0ms

Steps
ItersRangePoint
9
6.917170890574944e+107
5.265450304694307e+113
2.3413605341108193e+111
8
2.526907491460513e-81
1.0656496552560445e-78
3.141274979976896e-81
9
1.3614121906554968e-102
1.7460013876529985e-96
1.4298219294769426e-96
9
2.340612854427327e-138
4.914027131902431e-132
2.5666828723111e-133
7
1.132824888943737e-194
7.128468305309249e-193
4.068654166237997e-193
9
5.728645780898564e-301
1.1467953016179043e-293
1.0545681612574828e-300
8
-8.884549319778682e-241
-1.7577155122994853e-243
-8.097842811387573e-243
7
-9.954700830183718e-146
-8.477397266098905e-148
-9.677770542110421e-147
8
-3.505913724620813e-95
-6.071646318462641e-99
-2.6288074934322422e-95
7
-1.0229816341991673e-41
-1.6287520886102516e-43
-1.3075851156243092e-42

simplify17.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
080204
1103204
2108204
3109204
done109204

end0.0ms

sample742.0ms

Algorithm
intervals
Results
212.0ms6038×body80valid
132.0ms694×body2560valid
81.0ms512×body1280valid
75.0ms298×body5120valid
30.0ms244×body640valid
14.0ms138×body320valid
5.0ms76×body160valid