Details

Time bar (total: 2.9s)

sample20.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize10.0ms

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))
27.3b
(/ (- (* x.im y.re) (* x.re 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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
85.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0292541
11273493
25002491

prune175.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
16.8b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
7.0ms
(- (* x.im y.re) (* x.re y.im))
9.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* x.im y.re) (* x.re y.im))
116.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0304910
1990857
23354845
35001845

prune297.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
16.9b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
32.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×sqrt-div add-log-exp
5×unswap-sqr
4×prod-exp
3×flip3-- flip3-+ associate-*l* flip-- flip-+
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv sub-neg rec-exp diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
3.0ms
(- (* x.im y.re) (* x.re y.im))
18.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
118.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0378916
11785831
25001807

prune294.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))
15.3b
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
18.4b
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
6×times-frac associate-/r*
4×pow1 cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
2×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
4.0ms
(+ (* y.re y.re) (* y.im y.im))
6.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

series145.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
26.0ms
(+ (* y.re y.re) (* y.im y.im))
48.0ms
(/ (* x.im y.re) (+ (* y.re y.re) (* y.im y.im)))
45.0ms
(/ (* x.re y.im) (+ (* y.re y.re) (* y.im y.im)))

simplify42.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0309530
11570442
25001438

prune188.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 23.7b

regimes120.0ms

Accuracy

40% (1.5b remaining)

Error of 23.7b against oracle of 22.1b and baseline of 24.7b

bsearch109.0ms

Steps
ItersRangePoint
9
6.632739157271252e+62
1.647935043894467e+68
3.4366687886863465e+63
10
-1.1492159344471653e-16
-6.899281251030229e-31
-4.002330886974353e-17

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03728
13728

end0.0ms

sample522.0ms

Algorithm
intervals
Results
294.0ms8451×body80valid