Details

sample272.0ms

Algorithm

intervals

Results

202.0ms	172×	body	1280	valid
43.0ms	58×	body	640	valid
5.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	4×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	41	18
done	41	18

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.9b

localize25.0ms

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)
1.6b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.7b	(cos (- lambda1 lambda2))

rewrite28.0ms

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:

15.0ms	(* (* (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))

series173.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(* (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)))))
17.0ms	(cos (- lambda1 lambda2))

simplify5.8s

Counts

86 → 86

Iterations

Useful iterations: done (5.8s)

Iter	Nodes	Cost
0	196	1763
1	384	1589
2	1016	1325
3	2837	1281
4	4965	1208
done	5000	1190

prune405.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
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)
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
1.5b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
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)
14.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (sin lambda2))
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)
104.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
16.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify2.8s

Counts

90 → 90

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	143	2023
1	320	1773
2	1048	1429
3	4449	1429
done	5000	1429

prune554.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
1.5b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
14.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))))) R)
105.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
17.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (log1p (expm1 (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))))

simplify2.7s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	146	2111
1	321	1963
2	1030	1467
3	4461	1429
done	5000	1429

prune572.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
0.3b	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
1.0b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
1.5b	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

6.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
1.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
1.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
0.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))) R)
32.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2))))))
12.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))))
14.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)))))

simplify3.7s

Counts

78 → 78

Iterations

Useful iterations: 5 (512.0ms)

Iter	Nodes	Cost
0	98	2330
1	152	2225
2	286	2059
3	508	1971
4	795	1971
5	1533	1969
6	4688	1969
done	5001	1969

prune414.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.0b

regimes1.0s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	31	33
done	31	33

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4802×	body	1280	valid
1.4s	2068×	body	640	valid
318.0ms	686×	body	320	valid
87.0ms	281×	body	160	valid
30.0ms	10×	body	2560	valid
23.0ms	156×	body	80	valid