Details

Time bar (total: 29.3s)

sample355.0ms

Algorithm
intervals
Results
118.0ms250×body80valid
97.0ms63×body1280valid
19.0ms28×body640valid
6.0ms18×body320valid
1.0ms6×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

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:
24.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
14.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
34.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
237.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify886.0ms

Counts
109 → 109
Iterations

Useful iterations: done (882.0ms)

IterNodesCost
01831590
13481549
212191443
done50001436

prune797.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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:
1.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
12.0ms
(* (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)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
22.0ms
(* (atan2 x.im x.re) y.re)
30.0ms
(* (atan2 x.im x.re) y.im)
258.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0101729
1182720
2576638
34394630
done5000630

prune615.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize54.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (atan2 x.im x.re) y.im)
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (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)))
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series799.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (atan2 x.im x.re) y.im)
272.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
252.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
238.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts
62 → 62
Iterations

Useful iterations: 3 (502.0ms)

IterNodesCost
067800
1120794
2359702
32404696
done5000696

prune584.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize42.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.5b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

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×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 60
Calls
4 calls:
8.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (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)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
188.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
253.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.4s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
089756
1166748
2529664
33872656
done5001656

prune522.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.1b

regimes374.0ms

Accuracy

0% (0.5b remaining)

Error of 3.5b against oracle of 3.0b and baseline of 3.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01855
12655
22855
done2855

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s2010×body1280valid
1.9s7970×body80valid
1.8s1470×body640valid
422.0ms656×body320valid
150.0ms309×body160valid