Details

sample1.2s

Algorithm

intervals

Results

856.0ms	163×	body	1280	valid
142.0ms	54×	body	640	valid
29.0ms	25×	body	320	valid
4.0ms	7×	body	160	valid
2.0ms	7×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
3	34
2	33
1	26
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize94.0ms

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))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

45.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(* (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)))))
22.0ms	(cos (- lambda1 lambda2))

series315.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
94.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
47.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	2887
2	737
1	275
0	121

prune737.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize102.0ms

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))))))

rewrite105.0ms

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×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/`

Counts

4 → 70

Calls

4 calls:

19.0ms	(* (sin lambda1) (sin lambda2))
76.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
99.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
37.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify3.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
3	3880
2	979
1	320
0	144

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize108.0ms

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))))

rewrite41.0ms

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`
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 → 59

Calls

4 calls:

19.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
7.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin lambda2))
95.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
22.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
83.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
4	2438
3	1158
2	510
1	238
0	124

prune824.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite54.0ms

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`
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 → 58

Calls

4 calls:

34.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
5.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
9.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
101.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
40.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
38.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi2) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5008
6	3917
5	1629
4	1013
3	709
2	384
1	188
0	103

prune831.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample18.1s

Algorithm

intervals

Results

13.2s	4811×	body	1280	valid
3.4s	2069×	body	640	valid
635.0ms	678×	body	320	valid
158.0ms	303×	body	160	valid
84.0ms	132×	body	80	valid
60.0ms	12×	body	2560	valid