Details

sample135.0ms

Algorithm

intervals

Results

33.0ms	282×	body	80	valid
27.0ms	25×	body	1280	valid
19.0ms	39×	body	640	valid
10.0ms	26×	body	320	valid
3.0ms	13×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4415
4	917
3	240
2	69
1	32
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
33.3b	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

132×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip-+`

Counts

4 → 113

Calls

4 calls:

33.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))
10.0ms	(cos (/ (+ phi2 phi1) 2.0))
60.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0)))
34.0ms	(cos (/ (+ phi2 phi1) 2.0))
29.0ms	(cos (/ (+ phi2 phi1) 2.0))
832.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (cos (/ (+ phi2 phi1) 2.0))))))

simplify669.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
1	1330
0	444

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.1b

localize97.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
33.3b	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

19012×	`frac-times`
12960×	`cbrt-div`
10794×	`flip3--` `flip--`
8054×	`associate-*l/`
7776×	`cos-mult`
6446×	`associate-*r/`
5178×	`sqrt-div`
5176×	`frac-add`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 5212

Calls

4 calls:

32.0ms	(cos (/ (+ phi2 phi1) 2.0))
16.0ms	(cos (/ (+ phi2 phi1) 2.0))
16.0ms	(cos (/ (+ phi2 phi1) 2.0))
862.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

48.0ms	(cos (/ (+ phi2 phi1) 2.0))
39.0ms	(cos (/ (+ phi2 phi1) 2.0))
31.0ms	(cos (/ (+ phi2 phi1) 2.0))
1.0s	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

simplify9.9s

Counts

5224 → 5224

Iterations

Iter	Nodes
done	25063
0	25063

prune2.0m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.8b

localize85.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
6.0b	(exp (log (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))))
33.3b	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

38024×	`frac-times`
25920×	`cbrt-div`
21588×	`flip3--` `flip--`
16108×	`associate-*l/`
15552×	`cos-mult`
12892×	`associate-*r/`
10356×	`sqrt-div`
10352×	`frac-add`
5178×	`log-div` `exp-diff`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

4 → 10403

Calls

4 calls:

18.0ms	(cos (/ (+ phi2 phi1) 2.0))
8.0ms	(cos (/ (+ phi2 phi1) 2.0))
1.4s	(exp (log (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))))
582.0ms	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

series1.9s

Counts

4 → 12

Calls

4 calls:

29.0ms	(cos (/ (+ phi2 phi1) 2.0))
27.0ms	(cos (/ (+ phi2 phi1) 2.0))
667.0ms	(exp (log (sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))))
1.1s	(sqrt (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

simplify10.9s

Counts

10415 → 10415

Iterations

Iter	Nodes
done	41058
0	41058

prune3.1m

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 26.8b

localize98.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))
6.4b	(pow (exp 1/2) (log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))))))))
34.8b	(log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

38024×	`frac-times`
25920×	`cbrt-div`
21588×	`flip3--` `flip--`
16108×	`associate-*l/`
15552×	`cos-mult`
12892×	`associate-*r/`
10356×	`log-div`
10352×	`frac-add`
5178×	`pow-sub`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod`
5×	`add-exp-log`
4×	`pow-unpow` `pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-up` `exp-prod` `unpow-prod-down`
2×	`flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `sqr-pow`

Counts

4 → 10406

Calls

4 calls:

8.0ms	(cos (/ (+ phi2 phi1) 2.0))
17.0ms	(cos (/ (+ phi2 phi1) 2.0))
1.2s	(pow (exp 1/2) (log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))))))))
1.0s	(log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi2 phi1) 2.0))
27.0ms	(cos (/ (+ phi2 phi1) 2.0))
813.0ms	(pow (exp 1/2) (log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))))))))
614.0ms	(log (+ (* (- phi1 phi2) (- phi1 phi2)) (* (- lambda1 lambda2) (* (* (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))) (cbrt (* (- lambda1 lambda2) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))))))

simplify9.6s

Counts

10418 → 10418

Iterations

Iter	Nodes
done	33085
0	33085

prune3.0m

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 16.8b

regimes1.0s

Accuracy

51.1% (9.0b remaining)

Error of 29.9b against oracle of 20.9b and baseline of 39.3b

bsearch185.0ms

Steps

Iters	Range		Point
8	1.3203874505741148e+98	1.7551653436926632e+102	1.7253410160756383e+102
6	-5.51535315570543e+143	-4.022494018321081e+142	-3.1596332971703867e+143

simplify6.0ms

Iterations

Iter	Nodes
done	42
3	42
2	39
1	38
0	28

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	8313×	body	80	valid
774.0ms	791×	body	1280	valid
499.0ms	1290×	body	640	valid
242.0ms	751×	body	320	valid
57.0ms	351×	body	160	valid