Details

Time bar (total: 3.5s)

sample22.0ms

Algorithm
intervals
Results
11.0ms270×body80valid

simplify13.0ms

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: 27.7b

localize9.0ms

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)))

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:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
4.0ms
(- (* 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)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* y.re y.re) (* y.im y.im))
36.0ms
(- (* 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)))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0316555
11343496
25001481

prune183.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 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))
16.8b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

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:
12.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms
(- (* x.im y.re) (* x.re y.im))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series334.0ms

Counts
3 → 9
Calls
3 calls:
186.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms
(- (* x.im y.re) (* x.re y.im))
112.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05371099
12237907
25003905

prune267.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize10.0ms

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))
0.5b
(- (* x.im y.re) (* x.re y.im))
16.8b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite20.0ms

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:
8.0ms
(/ (/ (- (* 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))
6.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series260.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
38.0ms
(- (* x.im y.re) (* x.re y.im))
110.0ms
(/ (- (* 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

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt (hypot y.re y.im)))
0.5b
(- (* x.im y.re) (* x.re y.im))
8.0b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
9.1b
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
94×times-frac
66×*-un-lft-identity
60×add-cube-cbrt
53×sqrt-prod
32×add-exp-log
22×associate-*r* associate-*l*
20×add-cbrt-cube
15×unswap-sqr
12×associate-/r*
11×div-exp
8×pow1 prod-exp
6×cbrt-undiv associate-/l* add-log-exp
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp pow-flip 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 192
Calls
4 calls:
4.0ms
(/ 1 (sqrt (hypot y.re y.im)))
4.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
23.0ms
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ 1 (sqrt (hypot y.re y.im)))
39.0ms
(- (* x.im y.re) (* x.re y.im))
190.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))
118.0ms
(* (/ 1 (sqrt (hypot y.re y.im))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))

simplify83.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06742149
132141899
250021781

prune451.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

regimes182.0ms

Accuracy

33.3% (8.5b remaining)

Error of 12.7b against oracle of 4.2b and baseline of 17.0b

bsearch100.0ms

Steps
ItersRangePoint
11
9.199612759357812e+156
8.1420769820787e+178
1.0925783641640506e+158
10
-4.0387374422910434e+145
-4.657848749767963e+130
-5.157783051615335e+135

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215

end0.0ms

sample494.0ms

Algorithm
intervals
Results
293.0ms8451×body80valid