Details

sample704.0ms

Algorithm

intervals

Results

433.0ms	159×	body	1280	valid
134.0ms	61×	body	640	valid
26.0ms	23×	body	320	valid
6.0ms	8×	body	160	valid
2.0ms	5×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune64.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize64.0ms

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)
0.5b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b	(cos (- lambda1 lambda2))

rewrite85.0ms

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:

52.0ms	(* (* (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)))))
17.0ms	(cos (- lambda1 lambda2))

series334.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
62.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
47.0ms	(cos (- lambda1 lambda2))

simplify8.1s

Counts

86 → 86

Iterations

Useful iterations: done (8.1s)

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

prune607.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
0.5b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))

rewrite123.0ms

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:

14.0ms	(* (sin lambda2) (sin lambda1))
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))) R)
98.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
2.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin lambda2) (sin lambda1))
88.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))))) R)
305.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))
18.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))))

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	181	2086
1	473	1975
2	1852	1770
done	5000	1725

prune986.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.3b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.5b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
28.4b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cos-mult`
4×	`cube-div` `expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r*`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `frac-add` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-rgt-in` `acos-asin` `pow-to-exp` `distribute-lft-in` `pow1/3` `associate-l` `associate-l/` `-commutative` `rem-cbrt-cube`

Counts

4 → 84

Calls

4 calls:

98.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
13.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
24.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series445.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
96.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
19.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
63.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify2.1s

Counts

96 → 96

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	190	1892
1	501	1537
2	2058	1362
done	5000	1354

prune899.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))) R)
0.3b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))))
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))
0.5b	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))

rewrite43.0ms

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:

25.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))) R)
12.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))))
3.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))) R)
14.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))))
55.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2))))))
14.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))) (cos phi2)))))

simplify4.8s

Counts

78 → 78

Iterations

Useful iterations: 5 (823.0ms)

Iter	Nodes	Cost
0	100	2330
1	151	2225
2	297	1971
3	538	1971
4	834	1971
5	1671	1969
6	4909	1969
done	5000	1969

prune694.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.2b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	30	28
done	30	28

end0.0ms

sample18.9s

Algorithm

intervals

Results

13.9s	4750×	body	1280	valid
3.5s	2123×	body	640	valid
667.0ms	679×	body	320	valid
140.0ms	289×	body	160	valid
63.0ms	14×	body	2560	valid
39.0ms	146×	body	80	valid