Details

Time bar (total: 17.3s)

sample372.0ms

Algorithm
intervals
Results
42.0ms69×body1280valid
25.0ms55×body640valid
22.0ms256×body80valid
6.0ms22×body320valid
3.0ms16×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01937
13526
26325
39825
421525
585925
done500025

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
5.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (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)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) 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)
168.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
87 → 87
Iterations

Useful iterations: 3 (891.0ms)

IterNodesCost
01491444
13211414
29731207
343161200
done50001200

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
5.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
87 → 87
Iterations

Useful iterations: 3 (876.0ms)

IterNodesCost
01491444
13211414
29731207
343161200
done50001200

prune425.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
1.1b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
12×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
9.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (* (pow (hypot x.re x.im) y.re) (cbrt (pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3))) (exp (* (atan2 x.im x.re) y.im)))
19.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
147.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
87 → 87
Iterations

Useful iterations: 3 (916.0ms)

IterNodesCost
01531504
13291366
210021211
345291200
done50001200

prune476.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.9b

localize31.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite7.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
1.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
152.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
147.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
151.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
62 → 62
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
067800
1116794
2251702
3462696
4667696
51150696
62163696
done5000696

prune449.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.9b

regimes281.0ms

Accuracy

57% (2.1b remaining)

Error of 5.9b against oracle of 3.8b and baseline of 8.7b

bsearch4.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
033131
142131
done42131

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2058×body1280valid
696.0ms8020×body80valid
581.0ms1423×body640valid
201.0ms672×body320valid
61.0ms329×body160valid