Details

Time bar (total: 3.4s)

sample22.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947
done947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
25.5b
(/ (- (* 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)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
41.0ms
(- (* x.im y.re) (* x.re y.im))
90.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify36.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0316555
11343496
25001481
done5001481

prune178.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b
(- (* x.im y.re) (* x.re y.im))
16.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×prod-exp
26×add-cbrt-cube
25×add-sqr-sqrt
23×div-exp
22×times-frac
20×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×rec-exp
5×pow1 add-log-exp
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 110
Calls
3 calls:
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))

series347.0ms

Counts
3 → 9
Calls
3 calls:
184.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
41.0ms
(- (* x.im y.re) (* x.re y.im))
121.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify57.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05371095
12236907
25002905
done5002905

prune260.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

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))
0.5b
(- (* x.im y.re) (* x.re y.im))
16.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite51.0ms

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:
18.0ms
(/ (/ (- (* 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))
18.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series274.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
38.0ms
(- (* x.im y.re) (* x.re y.im))
118.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify49.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04511408
116591307
250011298
done50011298

prune305.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
17.0b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log
20×add-sqr-sqrt
17×add-cbrt-cube
14×*-un-lft-identity times-frac
13×add-cube-cbrt associate-*r*
9×div-exp
8×prod-exp
6×associate-/l/
5×pow1 cbrt-undiv flip3-- flip-- add-log-exp
4×frac-times associate-*l/ cbrt-unprod
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u unswap-sqr
2×rec-exp 1-exp associate-*r/ un-div-inv div-inv
1×sub-neg frac-2neg fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative associate-/l*
Counts
3 → 91
Calls
3 calls:
25.0ms
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
32.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

series279.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
38.0ms
(- (* x.im y.re) (* x.re y.im))
119.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (hypot y.re y.im)))

simplify48.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0410813
11822677
25002656
done5002656

prune205.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 6.1b

regimes226.0ms

Accuracy

26.4% (9.0b remaining)

Error of 13.9b against oracle of 4.9b and baseline of 17.2b

bsearch56.0ms

Steps
ItersRangePoint
10
4.798752560252719e+112
3.8564235113666274e+122
3.2100008695553146e+117
6
-7.922501144416864e+66
-5.906598016548616e+65
-7.723814496095852e+66

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02412
12512
22512
done2512

end0.0ms

sample580.0ms

Algorithm
intervals
Results
286.0ms8466×body80valid