Details

sample454.0ms

Algorithm

intervals

Results

307.0ms	152×	body	1280	valid
63.0ms	70×	body	640	valid
14.0ms	25×	body	320	valid
3.0ms	9×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (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)))))
3.1b	(cos (- lambda1 lambda2))

rewrite96.0ms

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:

50.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
34.0ms	(cos (- lambda1 lambda2))

series622.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
404.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
40.0ms	(cos (- lambda1 lambda2))

simplify7.7s

Counts

86 → 86

Iterations

Useful iterations: done (7.7s)

Iter	Nodes	Cost
0	196	1763
1	377	1589
2	962	1325
3	2320	1281
4	3808	1190
done	5001	1144

prune608.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.6b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite117.0ms

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:

14.0ms	(* (sin lambda1) (sin lambda2))
89.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
11.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
90.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
26.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify3.9s

Counts

90 → 90

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	143	2023
1	303	1773
2	1016	1429
3	4029	1429
done	5000	1429

prune903.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))))) R)
0.3b	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
1.6b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
27.7b	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`cube-div`
5×	`pow-pow` `pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l`
2×	`cube-mult` `frac-times` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `associate-l/` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

14.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))))) R)
79.0ms	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
5.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
50.0ms	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

series598.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))))) R)
274.0ms	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
26.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
165.0ms	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

simplify1.0s

Counts

100 → 100

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	171	2552
1	393	2223
2	1369	1768
done	5000	1729

prune993.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.2b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
1.6b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite33.0ms

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:

22.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
2.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
6.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
43.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
22.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
13.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify5.4s

Counts

78 → 78

Iterations

Useful iterations: 5 (925.0ms)

Iter	Nodes	Cost
0	93	2330
1	140	2225
2	274	1971
3	489	1971
4	801	1971
5	1660	1969
6	4945	1969
done	5000	1969

prune650.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 4.2b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample19.7s

Algorithm

intervals

Results

14.3s	4768×	body	1280	valid
3.2s	2136×	body	640	valid
739.0ms	682×	body	320	valid
491.0ms	13×	body	2560	valid
147.0ms	266×	body	160	valid
36.0ms	136×	body	80	valid