Details

Time bar (total: 16.8s)

sample30.0ms

Algorithm
intervals
Results
17.0ms265×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
27.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
11.0ms
(+ (* x.re y.re) (* x.im y.im))
53.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series153.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(+ (* x.re y.re) (* x.im y.im))
117.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts
53 → 53
Iterations

Useful iterations: 3 (719.0ms)

IterNodesCost
090972
1245818
2830747
32687743
done5001743

prune203.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
0.3b
(fma y.re x.re (* x.im y.im))
16.2b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp 1-exp
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(hypot y.re y.im)
30.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
1.0ms
(fma y.re x.re (* x.im y.im))
8.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series507.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot y.re y.im)
255.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
63.0ms
(fma y.re x.re (* x.im y.im))
139.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify3.5s

Counts
119 → 119
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01461955
13391821
210831579
340011579
done50001546

prune433.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b
(fma y.re x.re (* x.im y.im))
16.2b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.re y.im)
17.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma y.re x.re (* x.im y.im))
8.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series413.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot y.re y.im)
156.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
51.0ms
(fma y.re x.re (* x.im y.im))
153.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify2.2s

Counts
133 → 133
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01672544
13332481
27142298
320502244
done50002182

prune681.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(/ (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
0.3b
(fma y.re x.re (* x.im y.im))
16.3b
(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
21×add-sqr-sqrt
18×add-cbrt-cube
15×*-un-lft-identity
14×add-cube-cbrt times-frac
13×associate-*r*
9×div-exp
8×prod-exp
6×pow1
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×rec-exp 1-exp associate-*r/ un-div-inv div-inv associate-/l/
1×hypot-udef frac-2neg pow-prod-down clear-num *-commutative fma-udef associate-/l*
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot y.re y.im)
15.0ms
(/ (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
0.0ms
(fma y.re x.re (* x.im y.im))
15.0ms
(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(hypot y.re y.im)
142.0ms
(/ (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
50.0ms
(fma y.re x.re (* x.im y.im))
116.0ms
(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify4.2s

Counts
99 → 99
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01261415
12781252
27941032
330981018
done50001018

prune398.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

regimes222.0ms

Accuracy

37.4% (6.7b remaining)

Error of 12.6b against oracle of 6.0b and baseline of 16.6b

bsearch85.0ms

Steps
ItersRangePoint
7
5.026165092204197e+184
4.358401358984652e+186
1.5430679091287252e+185
9
-9.137650963602708e+166
-1.1971825537892871e+162
-5.286331128515371e+162

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02239
12633
done2633

end0.0ms

sample1.2s

Algorithm
intervals
Results
842.0ms8453×body80valid