Details

Time bar (total: 3.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms272×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* x.re y.re) (* x.im y.im))
27.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series134.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
78.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify130.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune203.0ms

Filtered
70 candidates to 57 candidates (81.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
17.6b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
92×prod-exp
63×div-exp
50×add-cbrt-cube
41×1-exp
17×cbrt-unprod
16×cbrt-undiv
15×rec-exp
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity times-frac
9×pow1
7×associate-*r* associate-*l*
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×pow-flip frac-2neg pow-prod-down clear-num associate-/r*
1×frac-times hypot-udef associate-*r/ associate-*l/ *-commutative inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
0.0ms
(hypot y.re y.im)
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
24.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series396.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot y.re y.im)
56.0ms
(/ 1 (* (hypot y.re y.im) 1))
182.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
112.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify50.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04931177
11635880
25001872

prune293.0ms

Filtered
157 candidates to 79 candidates (50.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
17.6b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×hypot-udef frac-2neg 1-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
6.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series331.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot y.re y.im)
46.0ms
(hypot y.re y.im)
121.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
113.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify76.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0301780
11076689
23153689
35001681

prune330.0ms

Filtered
111 candidates to 90 candidates (81.1%)
Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(/ 1 (hypot y.re y.im))
0.1b
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
17.6b
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×add-cbrt-cube
27×add-sqr-sqrt
26×prod-exp
25×div-exp
21×*-un-lft-identity times-frac
20×add-cube-cbrt
13×associate-*r*
10×cbrt-undiv 1-exp
9×cbrt-unprod
7×pow1
5×rec-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×associate-*l* div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num un-div-inv associate-/l/
1×hypot-udef pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 119
Calls
4 calls:
0.0ms
(hypot y.re y.im)
2.0ms
(/ 1 (hypot y.re y.im))
7.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
8.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot y.re y.im)
52.0ms
(/ 1 (hypot y.re y.im))
120.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
113.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify45.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0398858
11608678
25001651

prune266.0ms

Filtered
131 candidates to 74 candidates (56.5%)
Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.5b

regimes226.0ms

Accuracy

33.4% (7.4b remaining)

Error of 13.1b against oracle of 5.7b and baseline of 16.8b

bsearch60.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
3.559188999299462e+84
8
-1.6993806662071022e+156
-3.922170094862376e+153
-3.776971399950804e+155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample517.0ms

Algorithm
intervals
Results
305.0ms8456×body80valid