Details

Time bar (total: 5.3s)

sample38.0ms

Algorithm
intervals
Results
27.0ms268×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: 26.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(- (* x.im y.re) (* x.re y.im))
26.2b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
36.0ms
(- (* x.im y.re) (* x.re y.im))
84.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0316555
11343496
25001481

prune194.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(- (* x.im y.re) (* x.re y.im))
0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
15.3b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite46.0ms

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:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
3.0ms
(- (* x.im y.re) (* x.re y.im))
24.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series392.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (* (hypot y.re y.im) 1))
40.0ms
(- (* x.im y.re) (* x.re y.im))
185.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
116.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify66.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05551207
123061003
25003995

prune318.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.2b
(- (* x.im y.re) (* x.re y.im))
15.3b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
5×add-log-exp
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 99
Calls
3 calls:
10.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series269.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
39.0ms
(- (* x.im y.re) (* x.re y.im))
112.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify47.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0423962
11691852
25001851

prune276.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
0.2b
(- (* x.im y.re) (* x.re y.im))
7.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
7.9b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
892×times-frac
402×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
384×sqrt-prod
161×associate-/l*
41×add-exp-log
32×add-cbrt-cube
24×div-inv
22×div-exp
16×cbrt-undiv
13×associate-/r*
6×div-sub prod-exp add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg 1-exp clear-num cbrt-unprod
2×flip3-- flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 540
Calls
4 calls:
39.0ms
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
3.0ms
(- (* x.im y.re) (* x.re y.im))
11.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
14.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (* (hypot y.re y.im) 1))
38.0ms
(- (* x.im y.re) (* x.re y.im))
190.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
326.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))

simplify101.0ms

Algorithm
egg-herbie
Counts
552 → 552
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013769380
150028406

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.3b

regimes258.0ms

Accuracy

30.7% (8.8b remaining)

Error of 13.2b against oracle of 4.4b and baseline of 17.1b

bsearch107.0ms

Steps
ItersRangePoint
9
3.2605516108797835e+130
1.2684932886978702e+137
7.513255736758786e+136
10
-4.68496613899928e+225
-6.299496552493713e+213
-6.40315436234457e+213

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215

end0.0ms

sample996.0ms

Algorithm
intervals
Results
773.0ms8429×body80valid