Details

Time bar (total: 3.7s)

sample24.0ms

Algorithm
intervals
Results
12.0ms278×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: 22.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
22.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
10.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series130.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
76.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify136.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune201.0ms

Filtered
70 candidates to 57 candidates (81.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

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)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.3b
(fma x.re y.re (* x.im y.im))
12.9b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite33.0ms

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 associate-*r/ associate-*l/ *-commutative fma-udef inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
20.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms
(fma x.re y.re (* x.im y.im))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series375.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (* (hypot y.re y.im) 1))
175.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
39.0ms
(fma x.re y.re (* x.im y.im))
110.0ms
(/ (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 (33.0ms)

IterNodesCost
04861191
11654892
25002884

prune283.0ms

Filtered
157 candidates to 77 candidates (49.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.3b
(fma x.re y.re (* x.im y.im))
12.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite11.0ms

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
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×fma-udef associate-/l/
Counts
3 → 89
Calls
3 calls:
6.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series260.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
40.0ms
(fma x.re y.re (* x.im y.im))
108.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify76.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune254.0ms

Filtered
98 candidates to 76 candidates (77.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.3b
(fma x.re y.re (* x.im y.im))
12.9b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
159×times-frac
120×div-exp
112×prod-exp
105×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
64×1-exp
47×add-cbrt-cube
44×associate-*r*
43×rec-exp
19×cbrt-undiv
16×associate-/r*
12×pow1 cbrt-unprod
11×div-inv
7×associate-*l*
6×associate-/l*
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 270
Calls
4 calls:
5.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
35.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
181.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
35.0ms
(fma x.re y.re (* x.im y.im))
87.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
010202692
139782350
250022153

prune481.0ms

Filtered
282 candidates to 141 candidates (50.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes164.0ms

Accuracy

32.2% (7.8b remaining)

Error of 13.5b against oracle of 5.8b and baseline of 17.2b

bsearch80.0ms

Steps
ItersRangePoint
8
3.905534790569565e+76
3.5318877144286925e+79
3.47490452119893e+79
10
-8.119291710401494e+188
-2.6279527955229556e+170
-9.255264963641289e+170

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample500.0ms

Algorithm
intervals
Results
292.0ms8480×body80valid