Details

Time bar (total: 17.5s)

sample417.0ms

Algorithm
intervals
Results
36.0ms37×body640valid
29.0ms52×body1280valid
21.0ms258×body80valid
6.0ms21×body320valid
3.0ms15×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (atan2 x.im x.re) y.im)
0.7b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.2b
(* (atan2 x.im x.re) y.re)
29.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(/ (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)
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
133.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
22.0ms
(* (atan2 x.im x.re) y.re)
171.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts
109 → 109
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01831590
13331549
28381441
324251436
done50001435

prune455.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (hypot x.re x.im)) y.re)
0.7b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
29.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
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:
104.0ms
(* (log (hypot x.re x.im)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)
160.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts
83 → 83
Iterations

Useful iterations: 3 (350.0ms)

IterNodesCost
0118748
1227733
2564645
3976641
41406641
52707641
done5000641

prune327.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
0.7b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
29.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.re)
160.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts
73 → 73
Iterations

Useful iterations: 3 (248.0ms)

IterNodesCost
0104761
1184747
2405657
3682653
4938653
51612653
63534653
done5001653

prune308.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
0.6b
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
1.2b
(* (atan2 x.im x.re) y.re)
29.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log
10×add-sqr-sqrt
9×add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
6×associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×*-commutative unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 62
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
0.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
6.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
223.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
17.0ms
(* (atan2 x.im x.re) y.re)
152.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
74 → 74
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
0116880
1228863
2567748
31202740
42171727
done5001727

prune354.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.3b

regimes158.0ms

Accuracy

0% (0.4b remaining)

Error of 3.2b against oracle of 2.8b and baseline of 3.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02338
12838
done2838

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2040×body1280valid
651.0ms8013×body80valid
530.0ms1407×body640valid
163.0ms636×body320valid
69.0ms346×body160valid