Details

sample288.0ms

Algorithm

intervals

Results

201.0ms	152×	body	1280	valid
50.0ms	64×	body	640	valid
18.0ms	25×	body	320	valid
2.0ms	11×	body	80	valid
1.0ms	4×	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: 12.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.8b	(sin (- lambda1 lambda2))

rewrite44.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune424.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite41.0ms

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` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (cos phi1) (sin phi2))
14.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
127.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	512	984
1	1910	801
2	5001	797

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
19.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
45.0ms	(* (sin lambda1) (sin lambda2))
130.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
173.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify76.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	579	1014
1	2808	885
2	5001	883

prune629.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
34×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod`
7×	`cos-mult`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`sin-mult`
2×	`cube-div` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `associate-r/` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`
1×	`pow2` `swap-sqr`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
14.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series286.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
103.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
57.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
60.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	444	681
1	2242	633
2	5001	631

prune645.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes365.0ms

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	47	52
1	47	52

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.2s	4625×	body	1280	valid
1.6s	1920×	body	640	valid
267.0ms	557×	body	320	valid
98.0ms	677×	body	80	valid
71.0ms	221×	body	160	valid