Details

Time bar (total: 14.3s)

sample28.0ms

Algorithm
intervals
Results
12.0ms267×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
25.3b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

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:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
41.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series167.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(+ (* x.re y.re) (* x.im y.im))
107.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts
53 → 53
Iterations

Useful iterations: 3 (868.0ms)

IterNodesCost
090972
1247818
2964747
34305743
done5000743

prune351.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y.re x.re (* x.im y.im))
0.0b
(/ 1 (hypot y.re y.im))
0.3b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
13.5b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
0.0ms
(fma y.re x.re (* x.im y.im))
9.0ms
(/ 1 (hypot y.re y.im))
40.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
6.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series578.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma y.re x.re (* x.im y.im))
76.0ms
(/ 1 (hypot y.re y.im))
296.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
129.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify2.4s

Counts
142 → 142
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01532192
14052083
230921777
done50021759

prune809.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re x.re (* x.im y.im))
0.1b
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
13.5b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
3 → 111
Calls
3 calls:
0.0ms
(fma y.re x.re (* x.im y.im))
12.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
5.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series365.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(fma y.re x.re (* x.im y.im))
169.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
138.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify1.0s

Counts
120 → 120
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01602484
13512423
216542254
done50002208

prune733.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y.re x.re (* x.im y.im))
0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))) (hypot y.re y.im))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
13.5b
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 319
Calls
4 calls:
1.0ms
(fma y.re x.re (* x.im y.im))
31.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))) (hypot y.re y.im))
16.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
10.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma y.re x.re (* x.im y.im))
260.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))) (hypot y.re y.im))
183.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
146.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

simplify1.1s

Counts
331 → 331
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04588797
113107962
done50017454

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes359.0ms

Accuracy

34.4% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.7b

bsearch107.0ms

Steps
ItersRangePoint
10
5.527224725001059e+164
3.61215045040521e+174
1.9188741816101593e+167
9
-3.6517455508645834e+196
-8.015590953485181e+188
-8.431905690361968e+188

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02035
12435
done2435

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s8517×body80valid