Details

sample512.0ms

Algorithm

intervals

Results

291.0ms	96×	body	1280	valid
140.0ms	59×	body	640	valid
21.0ms	22×	body	320	valid
20.0ms	68×	body	80	valid
6.0ms	11×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	55
3	55
2	54
1	35
0	22

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

10.0ms	(* (sin theta) (sin delta))
15.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
21.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
11.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin theta) (sin delta))
12.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
236.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
287.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2195
2	716
1	312
0	144

prune923.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize189.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.4b	(- (cos delta) (* (sin phi1) (sin (cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
0.4b	(* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
7.5b	(cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `rem-cbrt-cube` `flip--`

Counts

4 → 75

Calls

4 calls:

28.0ms	(* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
10.0ms	(- (cos delta) (* (sin phi1) (sin (cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
17.0ms	(* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
21.0ms	(cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
260.0ms	(- (cos delta) (* (sin phi1) (sin (cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
46.0ms	(* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
10.0ms	(cbrt (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify2.7s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	2066
2	798
1	314
0	118

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize273.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
7.5b	(cbrt (* (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-log-exp`

Counts

4 → 42

Calls

4 calls:

1.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
4.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
267.0ms	(cbrt (* (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
88.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
110.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
25.0ms	(cbrt (* (* (* (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify4.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
4	1304
3	420
2	168
1	93
0	54

prune859.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))
0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))
0.9b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log` `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` `cbrt-unprod` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

2.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))
22.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))))
11.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))
9.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))
222.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1)))))))
310.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))
291.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos theta) (cos phi1))))))))))

simplify2.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	1860
2	686
1	284
0	132

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes983.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample20.3s

Algorithm

intervals

Results

11.5s	3083×	body	1280	valid
5.0s	1902×	body	640	valid
1.4s	1984×	body	80	valid
959.0ms	720×	body	320	valid
647.0ms	311×	body	160	valid