Details

Time bar (total: 25.3s)

sample256.0ms

Algorithm
intervals
Results
93.0ms58×body640valid
49.0ms59×body1280valid
28.0ms254×body80valid
6.0ms16×body320valid
2.0ms10×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.8b

localize43.0ms

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)))
1.1b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
36.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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:
19.0ms
(/ (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)
13.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
35.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
228.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
109 → 109
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01831590
13331549
28331441
323981436
done50001435

prune788.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

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)))
1.1b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
36.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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 y.re (log (hypot x.re x.im)) (- (* (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)
6.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
22.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
240.0ms
(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 (402.0ms)

IterNodesCost
0110743
1202733
2474645
3956641
42069641
done5001641

prune537.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x.re x.im)
0.0b
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
1.8b
(* (atan2 x.im x.re) y.im)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×exp-prod associate-*r* associate-*l*
2×fma-udef
1×hypot-udef exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 54
Calls
4 calls:
0.0ms
(hypot x.re x.im)
2.0ms
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
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.im)

series419.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(hypot x.re x.im)
128.0ms
(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
207.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
25.0ms
(* (atan2 x.im x.re) y.im)

simplify3.5s

Counts
66 → 66
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
093691
1171675
2377598
3863586
42660585
done5000585

prune421.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (cos (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)
1.8b
(* (atan2 x.im x.re) y.im)
36.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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)
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)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(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)
33.0ms
(* (atan2 x.im x.re) y.im)
242.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.2s

Counts
80 → 80
Iterations

Useful iterations: 3 (378.0ms)

IterNodesCost
0116936
1195889
2430788
3743784
41081784
52032784
64780784
done5000784

prune392.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.2b

regimes213.0ms

Accuracy

0% (1.0b remaining)

Error of 4.0b against oracle of 3.0b and baseline of 4.0b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01315
12113
22313
done2313

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.7s2003×body1280valid
1.1s1489×body640valid
976.0ms8000×body80valid
240.0ms628×body320valid
83.0ms301×body160valid