Details

sample632.0ms

Algorithm

intervals

Results

327.0ms	163×	body	1280	valid
75.0ms	54×	body	640	valid
61.0ms	25×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	7×	body	80	valid

simplify55.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite62.0ms

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:

24.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
21.0ms	(cos (- lambda1 lambda2))

series370.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
54.0ms	(cos (- lambda1 lambda2))

simplify3.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	3612
2	959
1	403
0	197

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
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-l/` `associate-r/`

Counts

4 → 78

Calls

4 calls:

15.0ms	(* (sin lambda1) (sin lambda2))
33.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
191.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
118.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify3.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	4494
2	1114
1	341
0	152

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.1b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite33.0ms

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` `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 → 67

Calls

4 calls:

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

series256.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin lambda1) (sin lambda2))
106.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
60.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
4	2656
3	1300
2	549
1	254
0	132

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
0.3b	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
0.5b	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
0.6b	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`fma-neg`
6×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`associate-r`
2×	`asin-acos` `flip3--` `associate-*l/` `flip--` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
78.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
1.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
37.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

445.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
191.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))) R)
13.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
74.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))

simplify3.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
3	2828
2	975
1	433
0	204

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.6b

regimes1.0s

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.2b and baseline of 3.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample16.3s

Algorithm

intervals

Results

12.2s	4811×	body	1280	valid
2.9s	2069×	body	640	valid
495.0ms	678×	body	320	valid
131.0ms	303×	body	160	valid
56.0ms	12×	body	2560	valid
30.0ms	132×	body	80	valid