Details

Time bar (total: 30.4s)

sample360.0ms

Algorithm
intervals
Results
81.0ms61×body1280valid
50.0ms257×body80valid
26.0ms30×body640valid
9.0ms15×body320valid
3.0ms8×body160valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5000
5823
4210
395
262
135
019

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.0b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
14.0ms
(* y.re (log (hypot x.re x.im)))
11.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* y.re (log (hypot x.re x.im)))
21.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
155.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts
93 → 93
Iterations
IterNodes
done5000
43768
31505
2616
1270
0142

prune838.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.0b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef sin-sum log1p-expm1 fma-udef
Counts
4 → 65
Calls
4 calls:
1.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
11.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
31.0ms
(* (atan2 x.im x.re) y.re)
31.0ms
(* (atan2 x.im x.re) y.im)
182.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.0s

Counts
77 → 77
Iterations
IterNodes
done5006
44440
31373
2500
1221
0118

prune672.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* y.re (log (hypot x.re x.im))))
1.0b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cbrt-prod sin-sum pow1/3 fma-udef
Counts
4 → 65
Calls
4 calls:
3.0ms
(cbrt (* y.re (log (hypot x.re x.im))))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(cbrt (* y.re (log (hypot x.re x.im))))
18.0ms
(* (atan2 x.im x.re) y.re)
26.0ms
(* (atan2 x.im x.re) y.im)
158.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts
77 → 77
Iterations
IterNodes
done5001
42689
31127
2496
1235
0130

prune828.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize116.0ms

Local error

Found 4 expressions with local error:

18.7b
(sin (* (atan2 x.im x.re) y.re))
19.1b
(cos (* (atan2 x.im x.re) y.re))
22.9b
(sin (* y.im (log (hypot x.re x.im))))
23.0b
(cos (* y.im (log (hypot x.re x.im))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×distribute-rgt-in cos-sum distribute-lft-in sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
12.0ms
(sin (* (atan2 x.im x.re) y.re))
11.0ms
(cos (* (atan2 x.im x.re) y.re))
9.0ms
(sin (* y.im (log (hypot x.re x.im))))
15.0ms
(cos (* y.im (log (hypot x.re x.im))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sin (* (atan2 x.im x.re) y.re))
71.0ms
(cos (* (atan2 x.im x.re) y.re))
149.0ms
(sin (* y.im (log (hypot x.re x.im))))
149.0ms
(cos (* y.im (log (hypot x.re x.im))))

simplify2.3s

Counts
64 → 64
Iterations
IterNodes
done5000
41441
3559
2280
1188
0134

prune756.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

regimes525.0ms

Accuracy

0% (0.3b remaining)

Error of 3.5b against oracle of 3.2b and baseline of 3.5b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done32
132
024

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.5s2190×body1280valid
2.3s1392×body640valid
2.0s7957×body80valid
450.0ms590×body320valid
181.0ms247×body160valid
158.0ms56×body2560valid