Details

Time bar (total: 6.6s)

sample365.0ms

Algorithm
intervals
Results
45.0ms70×body1280valid
22.0ms257×body80valid
17.0ms42×body640valid
7.0ms26×body320valid
3.0ms17×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
11.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune285.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
2.9b
(log (exp (* (atan2 x.im x.re) y.im)))
30.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* log-pow
5×add-log-exp
3×log-prod sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square exp-prod exp-to-pow flip3-+ rem-log-exp flip-+
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series160.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify105.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0247426
1716377
21692374
33958374
45001374

prune294.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* y.re (log x.im)) (log (exp (* (atan2 x.im x.re) y.im)))))
0.1b
(* y.re (log x.im))
1.2b
(* (atan2 x.im x.re) y.im)
2.9b
(log (exp (* (atan2 x.im x.re) y.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×log-prod
14×add-cube-cbrt *-un-lft-identity
10×pow1
8×add-exp-log exp-sum add-cbrt-cube
7×associate-*r* add-log-exp
6×distribute-rgt-in distribute-lft-in associate-*l* associate--l+
4×exp-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg exp-to-pow exp-diff diff-log rem-log-exp
Counts
4 → 78
Calls
4 calls:
12.0ms
(exp (- (* y.re (log x.im)) (log (exp (* (atan2 x.im x.re) y.im)))))
4.0ms
(* y.re (log x.im))
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(log (exp (* (atan2 x.im x.re) y.im)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(exp (- (* y.re (log x.im)) (log (exp (* (atan2 x.im x.re) y.im)))))
37.0ms
(* y.re (log x.im))
18.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(log (exp (* (atan2 x.im x.re) y.im)))

simplify59.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0267483
1813399
22665381
35001379

prune235.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

regimes267.0ms

Accuracy

70.7% (5.4b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 22.2b

bsearch325.0ms

Steps
ItersRangePoint
11
-4.0941303216342756e-300
9.591751876127112e-292
3.96130267399914e-310
7
-3.0488698330943634e-169
-2.4444541728186137e-171
-1.6437379089044384e-170
8
-2.925724657482853e-101
-1.1471991660770418e-104
-5.659063016506691e-103

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05240
16440
26440

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2032×body1280valid
703.0ms7994×body80valid
623.0ms1499×body640valid
185.0ms647×body320valid
51.0ms273×body160valid