Details

sample946.0ms

Algorithm

intervals

Results

399.0ms	79×	body	640	valid
397.0ms	147×	body	1280	valid
17.0ms	20×	body	320	valid
5.0ms	7×	body	160	valid
1.0ms	4×	body	80	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	17	635
1	27	610
2	38	610
3	44	610
4	46	610
done	46	610

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.6b	(cos (- lambda1 lambda2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
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:

42.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

series253.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
21.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
38.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

86 → 86

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	45428
1	401	42814
2	1502	40962
done	5000	40632

prune933.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.8b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
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:

61.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
61.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
20.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify3.1s

Counts

92 → 92

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	179	58656
1	497	55685
2	2737	55260
done	5001	55155

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))))
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
0.5b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
0.8b	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

21.0ms	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))))
3.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
5.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))))
53.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
26.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
26.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

simplify4.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (669.0ms)

Iter	Nodes	Cost
0	107	82233
1	185	76480
2	411	76398
3	1281	76279
4	3848	76279
done	5001	76279

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.1b

localize118.0ms

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 lambda1) (cos lambda2))) (cos phi2))))))) R)
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
0.5b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
0.8b	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
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` `unswap-sqr` `rem-exp-log`

Counts

4 → 66

Calls

4 calls:

28.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))) R)
3.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
5.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))) R)
62.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))))
13.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))))
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))

simplify3.9s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	99	73142
1	163	67150
2	441	67029
3	2580	66990
done	5000	66990

prune940.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.1b

regimes3.1s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	22	985
1	26	985
done	26	985

end0.0ms

sample18.3s

Algorithm

intervals

Results

12.9s	4851×	body	1280	valid
3.6s	2089×	body	640	valid
1.0s	678×	body	320	valid
222.0ms	246×	body	160	valid
45.0ms	7×	body	2560	valid
33.0ms	133×	body	80	valid