Details

Time bar (total: 28.6s)

sample269.0ms

Algorithm
intervals
Results
84.0ms257×body80valid
60.0ms73×body1280valid
28.0ms53×body640valid
10.0ms20×body320valid
4.0ms14×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.4b

localize39.0ms

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)
1.9b
(* (atan2 x.im x.re) y.im)
33.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

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:
25.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
15.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (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)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
24.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
292.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify987.0ms

Counts
109 → 109
Iterations

Useful iterations: done (982.0ms)

IterNodesCost
01831590
13481549
212191443
done50001436

prune805.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize50.0ms

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)
1.9b
(* (atan2 x.im x.re) y.im)
33.0b
(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:
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(* (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)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
21.0ms
(* (atan2 x.im x.re) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
261.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0110743
1207733
2642649
34763641
done5000641

prune603.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
1.7b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

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×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log1p-udef log1p-expm1 fma-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
11.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (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)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
373.0ms
(log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
20.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
287.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts
73 → 73
Iterations

Useful iterations: 3 (990.0ms)

IterNodesCost
0105761
1189751
2564657
33901653
done5000653

prune700.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
1.7b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 75
Calls
4 calls:
4.0ms
(pow (log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
7.0ms
(* (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)))

series820.0ms

Counts
4 → 12
Calls
4 calls:
566.0ms
(pow (log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) 3)
21.0ms
(* (atan2 x.im x.re) y.re)
26.0ms
(* (atan2 x.im x.re) y.im)
207.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify817.0ms

Counts
87 → 87
Iterations

Useful iterations: done (811.0ms)

IterNodesCost
01281144
13001085
21116943
done5000939

prune698.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

regimes480.0ms

Accuracy

0% (0.4b remaining)

Error of 3.4b against oracle of 3.0b and baseline of 3.4b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02234
12934
23134
done3134

end0.0ms

sample7.7s

Algorithm
intervals
Results
2.4s2030×body1280valid
2.3s7968×body80valid
1.2s1460×body640valid
550.0ms313×body160valid
481.0ms662×body320valid