Details

Time bar (total: 10.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms283×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(- (* x.im y.re) (* x.re y.im))
26.7b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
42.0ms
(- (* x.im y.re) (* x.re y.im))
93.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0316555
11343496
25001481

prune182.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.7b
(- (* x.im y.re) (* x.re y.im))
17.1b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
11.0ms
(/ 1 (* (hypot y.re y.im) 1))
51.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
8.0ms
(- (* x.im y.re) (* x.re y.im))
18.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series410.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (* (hypot y.re y.im) 1))
189.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
42.0ms
(- (* x.im y.re) (* x.re y.im))
126.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify62.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05551207
123061003
25003995

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.7b
(- (* x.im y.re) (* x.re y.im))
17.1b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite63.0ms

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
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
26.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
20.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series297.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
42.0ms
(- (* x.im y.re) (* x.re y.im))
127.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04511408
116591307
250011298

prune336.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
0.7b
(- (* x.im y.re) (* x.re y.im))
7.8b
(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
9.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
5774×times-frac
2456×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1317×sqrt-prod
171×div-inv
99×associate-/r*
50×add-exp-log
34×div-exp
32×add-cbrt-cube
28×associate-/l*
25×associate-/r/
19×cbrt-undiv
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×rec-exp frac-2neg 1-exp clear-num associate-/l/
2×flip3-- flip--
1×sub-neg fma-neg diff-log div-sub prod-diff
Counts
4 → 1855
Calls
4 calls:
66.0ms
(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
8.0ms
(- (* x.im y.re) (* x.re y.im))
17.0ms
(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
22.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
40.0ms
(- (* x.im y.re) (* x.re y.im))
171.0ms
(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
211.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

simplify422.0ms

Algorithm
egg-herbie
Counts
1867 → 1867
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500152495

prune5.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

regimes212.0ms

Accuracy

32.8% (8.4b remaining)

Error of 12.5b against oracle of 4.1b and baseline of 16.6b

bsearch57.0ms

Steps
ItersRangePoint
7
7.67208945889578e+120
1.962517469472653e+123
1.9212074770170307e+123
7
-1.6491850885404887e+162
-1.800530875751681e+160
-3.1523796531642566e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03315
14015
24315
34315

end0.0ms

sample583.0ms

Algorithm
intervals
Results
292.0ms8434×body80valid