Details

sample713.0ms

Algorithm

intervals

Results

394.0ms	93×	body	1280	valid
132.0ms	68×	body	640	valid
95.0ms	59×	body	80	valid
37.0ms	26×	body	320	valid
8.0ms	10×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

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

prune84.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1))
0.3b	(* (sin theta) (* (sin delta) (cos phi1)))
0.4b	(asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))
0.6b	(- (cos delta) (* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

27.0ms	(* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1))
56.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
1.0ms	(asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))
31.0ms	(- (cos delta) (* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1)))

series892.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1))
167.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
16.0ms	(asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))
357.0ms	(- (cos delta) (* (sin (asin (fma (* (sin delta) (cos phi1)) (cos theta) (* (cos delta) (sin phi1))))) (sin phi1)))

simplify5.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	5003
3	3067
2	1042
1	369
0	164

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize137.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))
0.2b	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
0.3b	(* (sin theta) (* (sin delta) (cos phi1)))
0.6b	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
5×	`fma-udef`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

1.0ms	(fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))
12.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
47.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
17.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

263.0ms	(fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))
318.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
167.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
365.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))

simplify5.5s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
3	3126
2	1035
1	368
0	154

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
0.3b	(* (sin theta) (* (sin delta) (cos phi1)))
0.6b	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
0.9b	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`log-prod`
6×	`associate-l` `prod-diff` `add-log-exp`
5×	`exp-sum`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod` `fma-udef` `log1p-expm1-u`
3×	`exp-prod` `fma-neg`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `associate-*r/` `rem-log-exp` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

23.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
69.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
18.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
26.0ms	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
158.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
358.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
397.0ms	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

simplify6.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3410
2	1157
1	421
0	186

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize141.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
0.6b	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
0.9b	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log` `log-prod` `add-cbrt-cube`
6×	`associate-r` `associate-l` `prod-diff` `add-log-exp`
5×	`exp-sum`
4×	`expm1-log1p-u` `log-pow` `fma-udef` `log1p-expm1-u`
3×	`exp-prod` `fma-neg`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--` `sin-mult`

Counts

4 → 88

Calls

4 calls:

31.0ms	(* (sin theta) (sin delta))
22.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
17.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
27.0ms	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (sin theta) (sin delta))
315.0ms	(* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1))))
345.0ms	(- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))
333.0ms	(log (exp (- (cos delta) (* (sin phi1) (fma (sin delta) (* (cos theta) (cos phi1)) (* (cos delta) (sin phi1)))))))

simplify5.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3274
2	1040
1	390
0	179

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes904.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample28.3s

Algorithm

intervals

Results

17.3s	3110×	body	1280	valid
6.2s	1886×	body	640	valid
2.0s	691×	body	320	valid
1.4s	1990×	body	80	valid
627.0ms	323×	body	160	valid