Details

Time bar (total: 18.4s)

sample433.0ms

Algorithm
intervals
Results
45.0ms78×body1280valid
43.0ms257×body80valid
19.0ms49×body640valid
4.0ms16×body320valid
1.0ms6×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.7b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.4b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×times-frac
12×unpow-prod-down
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cbrt-undiv pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
11.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
17.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
171.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
109 → 109
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01831590
13331549
28331441
323981436
done50001435

prune482.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize19.0ms

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)))
1.7b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.4b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×cos-sum
Counts
4 → 60
Calls
4 calls:
2.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
155.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
72 → 72
Iterations

Useful iterations: 3 (289.0ms)

IterNodesCost
0110743
1202733
2474645
3956641
42069641
done5001641

prune339.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
1.7b
(* (atan2 x.im x.re) y.re)
2.0b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.4b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
10×associate-*r* pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
7×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod *-commutative
2×unswap-sqr
1×cos-sum fma-udef
Counts
4 → 77
Calls
4 calls:
67.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
7.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
18.0ms
(* (atan2 x.im x.re) y.re)
87.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
159.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
89 → 89
Iterations

Useful iterations: 4 (2.6s)

IterNodesCost
01321085
12791064
2863839
32025768
43375748
done5001748

prune410.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
1.7b
(* (atan2 x.im x.re) y.re)
2.0b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.4b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
10×associate-*r* pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
7×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod *-commutative
2×unswap-sqr
1×cos-sum fma-udef
Counts
4 → 77
Calls
4 calls:
65.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
7.0ms
(* (atan2 x.im x.re) y.re)
24.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))) (cbrt y.im))
21.0ms
(* (atan2 x.im x.re) y.re)
81.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
158.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
89 → 89
Iterations

Useful iterations: 4 (2.5s)

IterNodesCost
01321085
12791064
2863839
32025768
43375748
done5001748

prune424.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

regimes179.0ms

Accuracy

0% (0.3b remaining)

Error of 3.2b against oracle of 2.9b and baseline of 3.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02237
13037
23837
34037
done4037

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s1980×body1280valid
813.0ms7999×body80valid
541.0ms1412×body640valid
162.0ms617×body320valid
51.0ms297×body160valid