Details

Time bar (total: 7.1s)

sample450.0ms

Algorithm
intervals
Results
67.0ms84×body1280valid
23.0ms254×body80valid
19.0ms50×body640valid
7.0ms26×body320valid
3.0ms15×body160valid

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.6b

localize34.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
165.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411
done5002411

prune376.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
95.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify82.0ms

Counts
89 → 89
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0320595
11020544
23156516
35001484
done5001484

prune317.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.3b
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
2.4b
(* (atan2 x.im x.re) y.im)
37.1b
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 78
Calls
4 calls:
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
3.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
7.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

series596.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
299.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
18.0ms
(* (atan2 x.im x.re) y.im)
138.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

simplify49.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0299737
11300693
25002683
done5002683

prune317.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (atan2 x.im x.re))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow1/3
Counts
4 → 59
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(cbrt (atan2 x.im x.re))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify69.0ms

Counts
71 → 71
Iterations

Useful iterations: 4 (64.0ms)

IterNodesCost
0171436
1380400
2862398
32336398
45003394
done5003394

prune372.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes197.0ms

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0249
1289
2289
done289

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2066×body1280valid
663.0ms7962×body80valid
521.0ms1410×body640valid
164.0ms631×body320valid
50.0ms293×body160valid