Details

Time bar (total: 25.5s)

sample508.0ms

Algorithm
intervals
Results
123.0ms58×body1280valid
84.0ms48×body640valid
66.0ms252×body80valid
37.0ms1×body2560valid
19.0ms20×body320valid
3.0ms5×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done2059
62059
5808
4197
382
253
131
019

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize108.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (atan2 x.im x.re) y.im)
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (atan2 x.im x.re) y.im)
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
72 → 72
Iterations
IterNodes
done2004
42004
3906
2432
1207
0102

prune645.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.0b

localize117.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.re)
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
210.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
72 → 72
Iterations
IterNodes
done2001
42001
3860
2413
1203
0100

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

localize89.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (atan2 x.im x.re))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow1/3
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(cbrt (atan2 x.im x.re))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
197.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
65 → 65
Iterations
IterNodes
done2023
52023
41528
3649
2322
1169
088

prune707.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

localize126.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (atan2 x.im x.re))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow1/3
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(cbrt (atan2 x.im x.re))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
197.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
65 → 65
Iterations
IterNodes
done2023
52023
41528
3649
2322
1169
088

prune721.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.0b

regimes564.0ms

Accuracy

76.8% (3.1b remaining)

Error of 22.8b against oracle of 19.8b and baseline of 33.0b

bsearch243.0ms

Steps
ItersRangePoint
9
-1.1974226794431701e-304
5.287973967575518e-307
-8.6257611592827e-311

simplify25.0ms

Iterations
IterNodes
done39
139
029

end0.0ms

sample11.8s

Algorithm
intervals
Results
4.8s2220×body1280valid
3.1s8005×body80valid
2.5s1453×body640valid
580.0ms540×body320valid
257.0ms70×body2560valid
126.0ms220×body160valid