Details

sample657.0ms

Algorithm

intervals

Results

341.0ms	147×	body	1280	valid
89.0ms	71×	body	640	valid
19.0ms	26×	body	320	valid
5.0ms	9×	body	160	valid
1.0ms	3×	body	80	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.2b	(cos (- lambda1 lambda2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 76

Calls

4 calls:

13.0ms	(* (sin phi1) (sin phi2))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
15.0ms	(cos (- lambda1 lambda2))

series219.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (sin phi1) (sin phi2))
56.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
55.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
4	3037
3	1335
2	624
1	339
0	191

prune926.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 76

Calls

4 calls:

19.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
69.0ms	(* (sin phi1) (sin phi2))
97.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
27.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
4	3154
3	1611
2	696
1	295
0	146

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.3b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.1b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp` `sin-mult`

Counts

4 → 71

Calls

4 calls:

16.0ms	(* (sin phi1) (sin phi2))
22.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
5.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin phi1) (sin phi2))
93.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
63.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.5s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
5	4764
4	2261
3	1214
2	561
1	251
0	133

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.5b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))) R)
0.4b	(exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
1.0b	(log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
1.3b	(acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

rewrite30.0ms

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` `insert-posit16` `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 → 70

Calls

4 calls:

16.0ms	(* (log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))) R)
4.0ms	(exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
6.0ms	(log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
1.0ms	(acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))) R)
422.0ms	(exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
10.0ms	(log (exp (acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
10.0ms	(acos (fma (* (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify3.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
5	1900
4	1106
3	644
2	347
1	167
0	108

prune821.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.5b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample16.5s

Algorithm

intervals

Results

11.5s	4691×	body	1280	valid
3.3s	2154×	body	640	valid
1.1s	756×	body	320	valid
127.0ms	265×	body	160	valid
89.0ms	20×	body	2560	valid
28.0ms	117×	body	80	valid