Details

Time bar (total: 3.9s)

sample23.0ms

Algorithm
intervals
Results
11.0ms265×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(- (* x.im y.re) (* x.re y.im))
28.6b
(/ (- (* x.im y.re) (* x.re 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
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:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* y.re y.re) (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
82.0ms
(/ (- (* 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

prune203.0ms

Filtered
73 candidates to 59 candidates (80.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize12.0ms

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)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b
(- (* x.im y.re) (* x.re y.im))
16.2b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
27.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series371.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (* (hypot y.re y.im) 1))
177.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
34.0ms
(- (* x.im y.re) (* x.re y.im))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify61.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05551207
123061003
25003995

prune358.0ms

Filtered
155 candidates to 94 candidates (60.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

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))
0.3b
(- (* x.im y.re) (* x.re y.im))
16.2b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

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:
10.0ms
(/ (/ (- (* 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))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series264.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
36.0ms
(- (* x.im y.re) (* x.re y.im))
114.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify46.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0423962
11691852
25001851

prune310.0ms

Filtered
108 candidates to 83 candidates (76.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
0.3b
(- (* x.im y.re) (* x.re y.im))
16.3b
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
171×times-frac
120×div-exp
112×prod-exp
109×add-sqr-sqrt
97×*-un-lft-identity
95×add-cube-cbrt
64×1-exp
50×associate-*r*
47×add-cbrt-cube
43×rec-exp
19×cbrt-undiv
18×associate-/r* associate-/r/
12×pow1 cbrt-unprod
11×div-inv
9×flip3-- flip--
7×associate-*l*
6×associate-/l* add-log-exp
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×inv-pow
2×frac-2neg clear-num
1×frac-times sub-neg fma-neg diff-log associate-*r/ prod-diff associate-*l/ un-div-inv *-commutative
Counts
4 → 292
Calls
4 calls:
9.0ms
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
46.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
3.0ms
(- (* x.im y.re) (* x.re y.im))
5.0ms
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
175.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))))
37.0ms
(- (* x.im y.re) (* x.re y.im))
88.0ms
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify101.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
011653311
147002898
250022690

prune532.0ms

Filtered
304 candidates to 155 candidates (51.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

regimes223.0ms

Accuracy

30.4% (8.1b remaining)

Error of 12.8b against oracle of 4.7b and baseline of 16.3b

bsearch64.0ms

Steps
ItersRangePoint
6
5.9650085156736504e+115
7.404582030866378e+116
1.893204804927783e+116
7
-2.1816453435796007e+113
-4.6350190348360025e+111
-3.1762758054120593e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215

end0.0ms

sample517.0ms

Algorithm
intervals
Results
304.0ms8422×body80valid