Details

sample244.0ms

Algorithm

intervals

Results

164.0ms	144×	body	1280	valid
46.0ms	69×	body	640	valid
9.0ms	20×	body	320	valid
5.0ms	19×	body	160	valid
3.0ms	1×	body	2560	valid
0.0ms	3×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	42	18
done	42	18

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b	(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

11.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
44.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
19.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

86 → 86

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	196	1763
1	391	1589
2	1170	1307
3	4765	1227
done	5000	1215

prune391.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (sin lambda2))
193.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
56.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify658.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	177	2086
1	473	1975
2	1952	1726
done	5000	1726

prune554.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
1.7b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
13.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
100.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
66.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
16.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify545.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (126.0ms)

Iter	Nodes	Cost
0	166	2336
1	433	2047
2	1609	1642
done	5000	1642

prune517.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
0.2b	(* (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
0.5b	(expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
1.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`*-commutative` `fma-udef`
1×	`distribute-rgt-in` `acos-asin` `expm1-log1p` `distribute-lft-in` `associate-*l/` `cos-mult` `expm1-udef` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

8.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
3.0ms	(* (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
0.0ms	(expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
101.0ms	(* (log1p (expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))) R)
50.0ms	(expm1 (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
11.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: 3 (453.0ms)

Iter	Nodes	Cost
0	136	2052
1	288	1982
2	1030	1699
3	4616	1698
done	5000	1698

prune364.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 3.0b

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	31
1	29	31
done	29	31

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.5s	4698×	body	1280	valid
1.4s	2164×	body	640	valid
307.0ms	690×	body	320	valid
80.0ms	290×	body	160	valid
56.0ms	16×	body	2560	valid
22.0ms	145×	body	80	valid