Details

Time bar (total: 31.2s)

sample271.0ms

Algorithm
intervals
Results
118.0ms67×body1280valid
41.0ms253×body80valid
28.0ms39×body640valid
8.0ms17×body320valid
4.0ms1×body2560valid
2.0ms5×body160valid

simplify2.6s

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.6b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite49.0ms

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 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 → 77
Calls
4 calls:
14.0ms
(* y.re (log (hypot x.re x.im)))
11.0ms
(* (atan2 x.im x.re) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* y.re (log (hypot x.re x.im)))
35.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
194.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
89 → 89
Iterations
IterNodes
done5003
31877
2640
1270
0138

prune950.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.6b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×expm1-log1p sin-sum fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
5.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(expm1 (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
33.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
173.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts
73 → 73
Iterations
IterNodes
done5000
43666
31220
2488
1220
0114

prune834.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize103.0ms

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))))
1.6b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

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×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 → 61
Calls
4 calls:
0.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
28.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
178.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts
73 → 73
Iterations
IterNodes
done5001
44462
31276
2498
1217
0114

prune826.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize193.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.5b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sin-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
10.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
167.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
172.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
166.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
62 → 62
Iterations
IterNodes
done5002
53662
41454
3557
2267
1128
071

prune860.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

regimes847.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.4s2195×body1280valid
2.6s7953×body80valid
1.5s1491×body640valid
475.0ms528×body320valid
191.0ms58×body2560valid
94.0ms277×body160valid