Details

sample279.0ms

Algorithm

intervals

Results

197.0ms	148×	body	1280	valid
55.0ms	66×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	8×	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

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

rewrite22.0ms

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:

6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series471.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (cos lambda1) (sin lambda2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	339	641
1	1438	552
2	5001	552

prune412.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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

Counts

4 → 89

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
46.0ms	(* (cos lambda1) (sin lambda2))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
181.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	513	1086
1	2383	947
2	5003	946

prune609.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))
27.4b	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`cube-div` `associate-l` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-*r/`
2×	`distribute-rgt-in` `cube-mult` `sub-neg` `unpow-prod-down` `flip3--` `pow-pow` `distribute-lft-in` `unpow3` `cube-prod` `pow-exp` `sin-neg` `cos-mult` `*-commutative` `distribute-rgt-neg-out` `frac-sub` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `cube-neg` `associate-*l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin (- lambda2)))
5.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
13.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))
3.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

series371.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin lambda1) (sin (- lambda2)))
76.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
184.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))))
57.0ms	(cbrt (pow (* (sin lambda1) (sin (- lambda2))) 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	468	1025
1	2164	894
2	5002	882

prune547.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes374.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	28
1	37	28

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4601×	body	1280	valid
1.5s	2010×	body	640	valid
272.0ms	557×	body	320	valid
94.0ms	633×	body	80	valid
60.0ms	199×	body	160	valid