Details

sample274.0ms

Algorithm

intervals

Results

193.0ms	145×	body	1280	valid
52.0ms	71×	body	640	valid
8.0ms	18×	body	320	valid
2.0ms	16×	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	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(sin (- lambda1 lambda2))
4.5b	(cos (- lambda1 lambda2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

11.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series333.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune366.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (sin lambda1) (cos lambda2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (sin lambda1) (cos lambda2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	333	481
1	1341	409
2	5001	409

prune444.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 83

Calls

4 calls:

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

series311.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (sin lambda1) (cos lambda2))
49.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	494	785
1	2343	680
2	5001	680

prune508.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

15.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
14.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series239.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
68.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
60.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
60.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify73.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	450	568
1	2270	532
2	5001	532

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes384.0ms

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	44	51
1	44	51

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4572×	body	1280	valid
1.5s	1952×	body	640	valid
291.0ms	583×	body	320	valid
98.0ms	686×	body	80	valid
61.0ms	207×	body	160	valid