Details

Time bar (total: 36.9s)

sample353.0ms

Algorithm
intervals
Results
110.0ms253×body80valid
91.0ms79×body1280valid
49.0ms56×body640valid
13.0ms22×body320valid
3.0ms9×body160valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
65780
5821
4208
395
262
135
019

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.2b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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:
7.0ms
(* 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)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* y.re (log (hypot x.re x.im)))
19.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
153.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts
93 → 93
Iterations
IterNodes
53262
41626
3898
2525
1256
0142

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.2b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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:
7.0ms
(* 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)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* y.re (log (hypot x.re x.im)))
32.0ms
(* (atan2 x.im x.re) y.re)
30.0ms
(* (atan2 x.im x.re) y.im)
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts
93 → 93
Iterations
IterNodes
53262
41626
3898
2525
1256
0142

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.2b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
1.7b
(* (atan2 x.im x.re) y.im)
32.4b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-exp-log
9×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×sin-sum pow1/3 fma-udef
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt y.re)
21.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series584.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(cbrt y.re)
104.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
18.0ms
(* (atan2 x.im x.re) y.im)
157.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.9s

Counts
80 → 80
Iterations
IterNodes
44995
31637
2650
1272
0130

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize110.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt y.re))
1.2b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
1.7b
(* (atan2 x.im x.re) y.im)
32.7b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (* (cbrt (cbrt y.re)) (cbrt (cbrt y.re))) (cbrt (cbrt y.re))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1 add-exp-log
9×cbrt-prod *-un-lft-identity add-cbrt-cube add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
1×sin-sum pow1/3 fma-udef
Counts
4 → 71
Calls
4 calls:
1.0ms
(cbrt (cbrt y.re))
23.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (* (cbrt (cbrt y.re)) (cbrt (cbrt y.re))) (cbrt (cbrt y.re))))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
438.0ms
(cbrt (cbrt y.re))
135.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
31.0ms
(* (atan2 x.im x.re) y.im)
167.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (* (cbrt (cbrt y.re)) (cbrt (cbrt y.re))) (cbrt (cbrt y.re))))))

simplify2.7s

Counts
83 → 83
Iterations
IterNodes
44475
31660
2669
1277
0141

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

regimes776.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
219
119
015

end0.0ms

sample11.5s

Algorithm
intervals
Results
4.1s2102×body1280valid
3.7s7927×body80valid
2.4s1414×body640valid
506.0ms509×body320valid
248.0ms51×body2560valid
137.0ms249×body160valid