Details

sample507.0ms

Algorithm

intervals

Results

261.0ms	90×	body	1280	valid
152.0ms	59×	body	640	valid
23.0ms	24×	body	320	valid
22.0ms	71×	body	80	valid
9.0ms	12×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	56	33
3	60	33
done	60	33

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

14.0ms	(* (sin theta) (sin delta))
23.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin theta) (sin delta))
223.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
251.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	139	1435
1	301	1369
2	1072	1231
done	5001	1229

prune631.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.7b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`log-prod`
4×	`log-pow`
3×	`exp-prod` `associate-r` `associate-l`
2×	`sub-neg` `exp-sum`
1×	`log-div` `asin-acos` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

38.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
12.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
285.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
293.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify731.0ms

Counts

69 → 69

Iterations

Useful iterations: done (727.0ms)

Iter	Nodes	Cost
0	129	1907
1	277	1801
2	973	1612
done	5001	1608

prune650.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.7b	(log (exp (/ (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
15×	`exp-prod`
12×	`pow1`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod` `swap-sqr` `associate-r` `associate-l`
2×	`asin-acos` `associate-/r/`
1×	`pow2` `log-div` `flip3-+` `pow-plus` `exp-diff` `div-sub` `rem-log-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
25.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
78.0ms	(log (exp (/ (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
227.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.3s	(log (exp (/ (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))))

simplify1.6s

Counts

83 → 83

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	205	4116
1	485	3820
2	2231	3363
done	5002	2841

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin delta) (* (cos delta) (cos theta)))
0.3b	(pow (sin phi1) 3)
0.3b	(pow (sin phi1) 3)
0.4b	(pow (sin phi1) 4)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `add-exp-log`
11×	`add-cbrt-cube`
9×	`unpow-prod-down` `pow-unpow`
6×	`cube-prod`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-l` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`cube-mult` `unpow3` `rem-cube-cbrt`
1×	`associate-r/` `associate-r` `cos-mult` `-commutative`

Counts

4 → 82

Calls

4 calls:

35.0ms	(* (sin delta) (* (cos delta) (cos theta)))
4.0ms	(pow (sin phi1) 3)
4.0ms	(pow (sin phi1) 3)
5.0ms	(pow (sin phi1) 4)

series279.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (sin delta) (* (cos delta) (cos theta)))
54.0ms	(pow (sin phi1) 3)
55.0ms	(pow (sin phi1) 3)
69.0ms	(pow (sin phi1) 4)

simplify1.1s

Counts

94 → 94

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	130	773
1	369	674
2	1464	605
done	5001	603

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes634.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify29.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	108
1	74	108
2	76	108
3	78	108
done	78	108

end0.0ms

sample19.9s

Algorithm

intervals

Results

13.4s	3191×	body	1280	valid
3.8s	1819×	body	640	valid
1.1s	686×	body	320	valid
598.0ms	1999×	body	80	valid
320.0ms	305×	body	160	valid