Details

Time bar (total: 28.0s)

sample266.0ms

Algorithm
intervals
Results
108.0ms67×body1280valid
41.0ms250×body80valid
18.0ms25×body640valid
7.0ms16×body320valid
2.0ms6×body160valid
2.0ms1×body2560valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01937
13137
25336
38536
422036
5102336
done500036

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (atan2 x.im x.re) y.im)
30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (atan2 x.im x.re) y.im)
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
269.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts
68 → 68
Iterations

Useful iterations: 3 (654.0ms)

IterNodesCost
098845
1202787
2554701
32840686
done5001686

prune544.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.2b

localize68.0ms

Local error

Found 4 expressions with local error:

30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
190.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
208.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
233.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
51 → 51
Iterations

Useful iterations: 3 (171.0ms)

IterNodesCost
0711005
1144975
2294851
3654842
41878842
done5001842

prune590.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.2b

localize68.0ms

Local error

Found 4 expressions with local error:

13.4b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×unpow-prod-down cube-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 59
Calls
4 calls:
13.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
72.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
256.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0961505
12101290
27721146
done50011144

prune626.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.2b

localize58.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
3.3b
(* (atan2 x.im x.re) y.im)
17.5b
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
30.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-sum flip-+
Counts
4 → 59
Calls
4 calls:
13.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
143.0ms
(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify6.0s

Counts
71 → 71
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0119708
1247674
2744600
34938587
done5001587

prune372.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 15.9b

regimes732.0ms

Accuracy

74.2% (5.1b remaining)

Error of 17.7b against oracle of 12.6b and baseline of 32.4b

bsearch337.0ms

Steps
ItersRangePoint
5
5.7738765874496774e-39
1.5015648387031057e-38
9.889429990153021e-39
8
5.659139357978101e-160
9.04262595679448e-156
1.6992435620564553e-158
7
-1.3752126218593197e-306
-4.0720559692658706e-308
-4.116395237885326e-308

simplify23.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
043127
159105
done59105

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.5s2178×body1280valid
1.8s1451×body640valid
1.8s7942×body80valid
445.0ms229×body160valid
301.0ms568×body320valid
111.0ms47×body2560valid