Details

Time bar (total: 6.6s)

sample362.0ms

Algorithm
intervals
Results
47.0ms80×body1280valid
23.0ms247×body80valid
19.0ms48×body640valid
5.0ms18×body320valid
3.0ms14×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.1b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

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:
4.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
136.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381

prune320.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite21.0ms

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:
4.0ms
(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)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series234.0ms

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)))
89.0ms
(* (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 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune300.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
6×add-exp-log sqrt-div add-cbrt-cube
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
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)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series126.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify66.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0145374
1428355
21017352
32145352
45002352

prune366.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize28.0ms

Local error

Found 4 expressions with local error:

33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
15×add-sqr-sqrt sqrt-prod
12×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×unpow-prod-down cube-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 74
Calls
4 calls:
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series143.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0187488
1546483
21786483
35001483

prune423.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

regimes368.0ms

Accuracy

67.6% (7.1b remaining)

Error of 10.7b against oracle of 3.6b and baseline of 25.4b

bsearch109.0ms

Steps
ItersRangePoint
9
-1.9551681257519828e-307
2.6835278337350452e-300
-1.786414519364885e-309

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03617
14817
24817

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2070×body1280valid
678.0ms7983×body80valid
556.0ms1420×body640valid
180.0ms634×body320valid
54.0ms297×body160valid