Details

Time bar (total: 3.9m)

sample6.7s

Algorithm
intervals
Results
6.4s1513×body10240exit
69.0ms256×body80valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
65642
5808
4197
382
253
131
019

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div insert-posit16 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 → 60
Calls
4 calls:
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (atan2 x.im x.re) y.im)
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
221.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
72 → 72
Iterations
IterNodes
53991
41648
3881
2431
1207
0102

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (- x.re)) y.im)
0.3b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×pow1
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×associate-*l*
6×associate-*r*
4×insert-posit16 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 log-pow flip-+
Counts
4 → 64
Calls
4 calls:
13.0ms
(* (log (- x.re)) y.im)
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (log (- x.re)) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
230.0ms
(sin (+ (* (log (- x.re)) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
44194
31303
2601
1282
0134

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize86.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (- x.re)))
0.6b
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
23×add-sqr-sqrt
19×pow1
16×*-un-lft-identity
14×add-cube-cbrt
9×swap-sqr
7×pow1/3 associate-*r* associate-*l* log-pow
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×sqrt-prod
2×sqrt-div pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow-plus pow1/2 sin-sum prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt (log (- x.re)))
9.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

series1.2s

Counts
4 → 12
Calls
4 calls:
514.0ms
(cbrt (log (- x.re)))
486.0ms
(* (cbrt (log (- x.re))) (cbrt (log (- x.re))))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
180.0ms
(sin (+ (* (* (cbrt (log (- x.re))) (cbrt (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
96 → 96
Iterations
IterNodes
43796
31311
2586
1287
0135

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (- x.re)))
0.5b
(* (log (- x.re)) (log (- x.re)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b
(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
20×log-prod
19×add-sqr-sqrt pow1
18×*-un-lft-identity
16×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in
7×log-pow
6×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube swap-sqr add-exp-log
4×cbrt-prod associate-*r* associate-*l* insert-posit16 add-log-exp
3×sqrt-prod
2×neg-mul-1 sqrt-div
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow-plus pow1/2 sin-sum pow1/3 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 89
Calls
4 calls:
2.0ms
(cbrt (log (- x.re)))
20.0ms
(* (log (- x.re)) (log (- x.re)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

series1.0s

Counts
4 → 12
Calls
4 calls:
506.0ms
(cbrt (log (- x.re)))
303.0ms
(* (log (- x.re)) (log (- x.re)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms
(sin (+ (* (cbrt (* (log (- x.re)) (log (- x.re)))) (* (cbrt (log (- x.re))) y.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
101 → 101
Iterations
IterNodes
44825
31752
2797
1345
0173

prune2.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

regimes620.0ms

Accuracy

44.3% (6.1b remaining)

Error of 11.3b against oracle of 5.2b and baseline of 16.1b

bsearch4.4s

Steps
ItersRangePoint
8
-7.063320310351034e-285
-8.140111738589185e-289
-7.38905381868575e-286
6
-2.8843562846489532e-272
-3.6821524667833534e-273
-4.094520758958395e-273
8
-8.080219459080949e+30
-7.912080403382165e+27
-8.008752982451583e+27

simplify21.0ms

Iterations
IterNodes
272
172
053

end0.0ms

sample3.4m

Algorithm
intervals
Results
3.3m46912×body10240exit
3.6s8000×body80valid