Details

Time bar (total: 8.4s)

sample424.0ms

Algorithm
intervals
Results
70.0ms80×body1280valid
44.0ms256×body80valid
31.0ms55×body640valid
9.0ms20×body320valid
4.0ms13×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.5b

localize31.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune310.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.4b

localize15.0ms

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)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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:
7.0ms
(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)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
87.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune293.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(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
11×pow1
10×add-sqr-sqrt
9×add-exp-log
7×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×sqrt-prod
4×sqrt-div add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum associate-*r* *-commutative unswap-sqr
Counts
4 → 57
Calls
4 calls:
9.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
134.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify137.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 4 (131.0ms)

IterNodesCost
0232495
1586443
21587439
34527432
45002431

prune366.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.3b

localize27.0ms

Local error

Found 4 expressions with local error:

5.0b
(cbrt (atan2 x.im x.re))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow1/3
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt (atan2 x.im x.re))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cbrt (atan2 x.im x.re))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 4 (60.0ms)

IterNodesCost
0155400
1329368
2726366
31987366
45001364

prune309.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.3b

regimes211.0ms

Accuracy

57.4% (6.8b remaining)

Error of 10.5b against oracle of 3.6b and baseline of 19.7b

bsearch222.0ms

Steps
ItersRangePoint
9
746745586.0898634
6.227860645484908e+16
1662515902.0527577
5
-6.762010107941126e-229
-2.4125340179110713e-229
-4.5055110260069696e-229

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05027
15827
25827

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.7s2146×body1280valid
1.3s7978×body80valid
837.0ms1442×body640valid
280.0ms655×body320valid
89.0ms303×body160valid