Details

Time bar (total: 30.4s)

sample243.0ms

Algorithm
intervals
Results
59.0ms82×body1280valid
56.0ms32×body320valid
31.0ms260×body80valid
27.0ms49×body640valid
2.0ms9×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize49.0ms

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)))

rewrite68.0ms

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:
17.0ms
(/ (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)
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)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
20.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
219.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
109 → 109
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01831590
13331549
28331441
323981436
done50001435

prune782.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

localize30.0ms

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)))

rewrite34.0ms

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)))
12.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (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)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
19.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
245.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (447.0ms)

IterNodesCost
0110743
1202733
2474645
3956641
42069641
done5001641

prune595.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize46.0ms

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)))

rewrite24.0ms

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:
1.0ms
(log1p (cos (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)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
358.0ms
(log1p (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
33.0ms
(* (atan2 x.im x.re) y.re)
28.0ms
(* (atan2 x.im x.re) y.im)
239.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.7s

Counts
73 → 73
Iterations

Useful iterations: 3 (371.0ms)

IterNodesCost
0105761
1181751
2400657
3672653
4928653
51600653
63521653
done5001653

prune944.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize52.0ms

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)))

rewrite35.0ms

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:
5.0ms
(log (exp (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)
15.0ms
(* (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)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(log (exp (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
23.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
267.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.3s

Counts
80 → 80
Iterations

Useful iterations: 3 (332.0ms)

IterNodesCost
0116936
1195889
2430788
3743784
41081784
52032784
64780784
done5000784

prune545.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.6b

regimes271.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01728
12428
22628
done2628

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.8s8022×body80valid
2.5s1893×body1280valid
1.1s1414×body640valid
546.0ms663×body320valid
153.0ms294×body160valid