Details

sample592.0ms

Algorithm

intervals

Results

457.0ms	149×	body	1280	valid
83.0ms	59×	body	640	valid
12.0ms	18×	body	320	valid
6.0ms	25×	body	80	valid
3.0ms	5×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
4	95
3	78
2	47
1	28
0	17

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`cos-sum` `sin-sum`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `sin-diff`

Counts

4 → 86

Calls

4 calls:

12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
30.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
11.0ms	(sin (- lambda1 lambda2))
13.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
110.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
42.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify787.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1239
1	392
0	203

prune830.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi2) (cos phi1))
0.2b	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-r` `associate-l` `prod-diff`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/` `sin-cos-mult`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 87

Calls

4 calls:

19.0ms	(* (sin phi2) (cos phi1))
45.0ms	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
33.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

series734.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin phi2) (cos phi1))
181.0ms	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
466.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

simplify884.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1716
1	487
0	227

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi2) (cos phi1))
0.2b	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
0.2b	(* (sin lambda2) (sin phi1))
0.2b	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`associate-*l/` `sin-mult`
1×	`flip3-+` `associate-*r/` `flip-+` `sin-cos-mult`

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (sin phi2) (cos phi1))
36.0ms	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
26.0ms	(* (sin lambda2) (sin phi1))
41.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin phi2) (cos phi1))
237.0ms	(* (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (- (sin lambda2)))) (cos phi2))
55.0ms	(* (sin lambda2) (sin phi1))
112.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

simplify911.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1690
1	392
0	168

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))) (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))))
18.2b	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
18.2b	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
18.2b	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`-un-lft-identity` `associate-l/` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div` `sin-mult`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

64.0ms	(* (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))) (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))))
15.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
18.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
33.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))) (cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2))))
211.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
228.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))
244.0ms	(cbrt (* (* (sin phi1) (sin lambda1)) (sin lambda2)))

simplify1.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1326
1	280
0	107

prune961.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes617.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	47
3	47
2	46
1	42
0	29

end0.0ms

sample20.7s

Algorithm

intervals

Results

15.3s	4571×	body	1280	valid
3.4s	1969×	body	640	valid
885.0ms	558×	body	320	valid
182.0ms	685×	body	80	valid
177.0ms	217×	body	160	valid