Details

sample1.3s

Algorithm

intervals

Results

684.0ms	64×	body	640	valid
508.0ms	110×	body	1280	valid
56.0ms	54×	body	80	valid
38.0ms	20×	body	320	valid
9.0ms	8×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	64
3	64
2	59
1	36
0	22

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(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))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite64.0ms

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:

12.0ms	(* (sin theta) (sin delta))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
33.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin theta) (sin delta))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
241.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
297.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
3	2501
2	887
1	353
0	166

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))
0.3b	(* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))
0.5b	(expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))
0.5b	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

1.0ms	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))
13.0ms	(* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))
0.0ms	(expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))
8.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))

series845.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))
229.0ms	(* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))
357.0ms	(expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))
248.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))

simplify2.0s

Counts

78 → 78

Iterations

Iter	Nodes
3	2584
2	858
1	322
0	147

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
0.3b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.3b	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
16.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
8.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))
6.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
199.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
218.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify4.9s

Counts

78 → 78

Iterations

Iter	Nodes
4	5068
3	1973
2	723
1	297
0	141

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize162.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
0.5b	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
0.5b	(* (* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))
0.6b	(* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow-plus` `pow-prod-up`
6×	`fma-neg` `associate-r` `prod-diff`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`sub-neg` `flip3--` `diff-log` `*-commutative` `flip--` `unswap-sqr`
1×	`pow3`

Counts

4 → 101

Calls

4 calls:

7.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
8.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
32.0ms	(* (* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))
13.0ms	(* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

252.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
289.0ms	(- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))
694.0ms	(* (* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1))))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))
496.0ms	(* (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))) (expm1 (- (cos delta) (* (sin (asin (fma (* (cos theta) (cos phi1)) (sin delta) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify4.2s

Counts

113 → 113

Iterations

Iter	Nodes
3	5392
2	1409
1	469
0	168

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes576.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample28.1s

Algorithm

intervals

Results

15.5s	3041×	body	1280	valid
8.3s	1926×	body	640	valid
2.0s	2019×	body	80	valid
1.5s	682×	body	320	valid
410.0ms	332×	body	160	valid