Details

sample258.0ms

Algorithm

intervals

Results

178.0ms	140×	body	1280	valid
49.0ms	63×	body	640	valid
6.0ms	14×	body	320	valid
4.0ms	33×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(sin (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
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×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(sin (- lambda1 lambda2))
14.0ms	(cos (- lambda1 lambda2))

series182.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
95.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	443	1004
1	1340	773
2	5001	771

prune421.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (sin lambda1) (cos lambda2))
11.0ms	(* (cos phi1) (sin phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))

series201.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (cos lambda2))
43.0ms	(* (cos phi1) (sin phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	462	787
1	1582	631
2	5001	629

prune522.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (sin lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
47.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (sin lambda1) (sin lambda2))
120.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
105.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	429	825
1	1850	647
2	5001	647

prune534.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.9b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
30×	`add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `sin-cos-mult` `log1p-expm1-u`
3×	`log-prod` `log-pow` `*-commutative` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (sin lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
48.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (sin lambda2))
119.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
106.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
109.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	363	894
1	1637	705
2	5001	705

prune495.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes485.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	43
1	39	43

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.9s	4525×	body	1280	valid
1.5s	2040×	body	640	valid
274.0ms	585×	body	320	valid
83.0ms	637×	body	80	valid
59.0ms	213×	body	160	valid