Details

sample1.1s

Algorithm

intervals

Results

830.0ms	110×	body	1280	valid
183.0ms	57×	body	640	valid
31.0ms	65×	body	80	valid
31.0ms	19×	body	320	valid
5.0ms	5×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	64
3	64
2	59
1	36
0	22

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (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)))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 76

Calls

4 calls:

23.0ms	(* (sin theta) (sin delta))
35.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin theta) (sin delta))
241.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
306.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
3	2002
2	896
1	355
0	166

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))
0.3b	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
0.4b	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`sin-sum`
7×	`pow1`
6×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `add-exp-log` `associate--r+` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l` `prod-diff`
2×	`asin-acos`
1×	`log-div` `sub-neg` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

40.0ms	(* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))
1.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
16.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))
7.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))
11.0ms	(asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))
280.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))
13.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
3	2000
2	970
1	407
0	190

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))) (+ (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `log-pow`
9×	`log-prod` `exp-prod`
7×	`pow1` `associate-/l/`
6×	`add-cbrt-cube` `add-exp-log` `sin-mult`
5×	`cos-mult`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`log-div` `asin-acos` `associate-/r*` `exp-diff` `rem-log-exp` `frac-sub`
2×	`associate-l/` `associate-r/` `associate-/r/` `sub-div`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 101

Calls

4 calls:

71.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))) (+ (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))))
3.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
4.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
14.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

978.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta))))))))))) (+ (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))))))
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
10.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

simplify2.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	2013
3	2013
2	1787
1	484
0	189

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize184.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
2.8b	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-pow`
12×	`add-sqr-sqrt` `log-prod` `exp-prod` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
4×	`expm1-log1p-u` `log-div` `asin-acos` `add-cbrt-cube` `exp-diff` `rem-log-exp` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

3.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
3.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
3.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
3.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
7.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))
6.0ms	(log (exp (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))))

simplify2.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	2013
9	2013
8	1703
7	566
6	277
5	166
4	124
3	105
2	89
1	78
0	57

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes792.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample27.8s

Algorithm

intervals

Results

16.6s	3124×	body	1280	valid
6.4s	1819×	body	640	valid
2.3s	717×	body	320	valid
1.6s	2045×	body	80	valid
463.0ms	295×	body	160	valid