Details

Time bar (total: 32.3s)

sample438.0ms

Algorithm
intervals
Results
163.0ms82×body1280valid
54.0ms260×body80valid
43.0ms49×body640valid
20.0ms32×body320valid
3.0ms9×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize36.0ms

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)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

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:
12.0ms
(/ (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)
7.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(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:
192.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
25.0ms
(* (atan2 x.im x.re) y.re)
41.0ms
(* (atan2 x.im x.re) y.im)
279.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts
109 → 109
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01831590
13331549
28331441
323981436
done50001435

prune773.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

localize29.0ms

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)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(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)
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)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
23.0ms
(* (atan2 x.im x.re) y.re)
28.0ms
(* (atan2 x.im x.re) y.im)
291.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (538.0ms)

IterNodesCost
0110743
1202733
2474645
3956641
42069641
done5001641

prune544.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize58.0ms

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)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(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×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))))
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)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
367.0ms
(log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
36.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
256.0ms
(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 (465.0ms)

IterNodesCost
0105761
1181751
2400657
3672653
4928653
51600653
63521653
done5001653

prune582.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(log (exp (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)
2.0b
(* (atan2 x.im x.re) y.im)
34.0b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×log-prod exp-prod
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×log-div exp-diff rem-log-exp
Counts
4 → 68
Calls
4 calls:
12.0ms
(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
21.0ms
(* (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)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
25.0ms
(* (atan2 x.im x.re) y.re)
26.0ms
(* (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)))

simplify5.7s

Counts
80 → 80
Iterations

Useful iterations: 3 (454.0ms)

IterNodesCost
0116936
1195889
2430788
3743784
41081784
52032784
64780784
done5000784

prune604.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.6b

regimes313.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01728
12428
22628
done2628

end1.0ms

sample8.3s

Algorithm
intervals
Results
3.0s1893×body1280valid
2.6s8022×body80valid
1.3s1414×body640valid
454.0ms663×body320valid
123.0ms294×body160valid