Details

sample675.0ms

Algorithm

intervals

Results

336.0ms	145×	body	1280	valid
131.0ms	68×	body	640	valid
28.0ms	31×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	5×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize62.0ms

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)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite41.0ms

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:

11.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms	(cos (- lambda1 lambda2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin phi1) (sin phi2))
61.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
29.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

88 → 88

Iterations

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

prune769.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.1b

localize113.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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` `insert-posit16` `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 → 84

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
79.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (sin lambda2))
240.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
81.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1973
1	525
0	193

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.9b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.5b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow` `cos-mult`
2×	`frac-times` `flip3-+` `associate-r/` `-commutative` `flip-+`
1×	`distribute-rgt-in` `acos-asin` `exp-prod` `distribute-lft-in` `exp-to-pow` `rem-log-exp` `associate-*l/` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

57.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
17.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
9.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
94.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
73.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify1.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1546
1	441
0	172

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))) R)
0.3b	(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))
1.1b	(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))))
1.5b	(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))

rewrite28.0ms

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:

20.0ms	(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))) R)
2.0ms	(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))
3.0ms	(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))))
1.0ms	(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))) R)
29.0ms	(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1)))))
17.0ms	(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))))
18.0ms	(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi2) (sin phi1))))

simplify4.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
5	4443
4	1814
3	796
2	333
1	168
0	109

prune735.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 5.9b

regimes2.1s

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample18.9s

Algorithm

intervals

Results

13.7s	4716×	body	1280	valid
3.8s	2166×	body	640	valid
693.0ms	695×	body	320	valid
150.0ms	271×	body	160	valid
57.0ms	11×	body	2560	valid
39.0ms	144×	body	80	valid