Details

sample830.0ms

Algorithm

intervals

Results

538.0ms	148×	body	1280	valid
135.0ms	80×	body	640	valid
20.0ms	16×	body	320	valid
6.0ms	6×	body	160	valid
4.0ms	1×	body	2560	valid
2.0ms	5×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	39
3	39
2	38
1	27
0	17

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize52.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.9b	(cos (- lambda1 lambda2))

rewrite51.0ms

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:

21.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms	(cos (- lambda1 lambda2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin phi1) (sin phi2))
67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
37.0ms	(cos (- lambda1 lambda2))

simplify2.4s

Counts

88 → 88

Iterations

Iter	Nodes
5	2884
4	1839
3	1055
2	591
1	329
0	191

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.4b

localize98.0ms

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 phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite159.0ms

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:

118.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
23.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* (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))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
58.0ms	(* (sin phi1) (sin phi2))
116.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.5s

Counts

96 → 96

Iterations

Iter	Nodes
3	9215
2	1942
1	533
0	195

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.3b

localize75.0ms

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 phi1) (sin phi2))
0.3b	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.6b	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite129.0ms

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:

85.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
30.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
81.0ms	(* (sin phi1) (sin phi2))
82.0ms	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
28.0ms	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.9s

Counts

96 → 96

Iterations

Iter	Nodes
3	9314
2	1963
1	538
0	196

prune2.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.3b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))) R)
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))
0.4b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))))
0.6b	(acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))

rewrite19.0ms

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:

10.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))) R)
4.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))
3.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))) R)
38.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2)))))
10.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))))
10.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (cos phi1)) (cos phi2))))

simplify3.8s

Counts

82 → 82

Iterations

Iter	Nodes
6	5010
5	1721
4	1001
3	701
2	368
1	174
0	110

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.3b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	35
1	35
0	28

end0.0ms

sample25.9s

Algorithm

intervals

Results

17.9s	4811×	body	1280	valid
5.6s	2123×	body	640	valid
1.6s	673×	body	320	valid
205.0ms	256×	body	160	valid
55.0ms	131×	body	80	valid
41.0ms	8×	body	2560	valid