Details

sample260.0ms

Algorithm

intervals

Results

189.0ms	145×	body	1280	valid
41.0ms	59×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	25×	body	80	valid
1.0ms	5×	body	160	valid

simplify9.0ms

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: 13.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite24.0ms

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:

4.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
101.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(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 phi1) (sin phi2))
7.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (sin phi1) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	303	481
1	1257	409
2	5002	409

prune424.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (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`
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 phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (sin phi1) (cos phi2))
49.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	480	785
1	2340	680
2	5001	680

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.2b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-exp-log` `add-cbrt-cube`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `associate-/r` `-commutative`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 190

Calls

4 calls:

90.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
73.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
14.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
508.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
58.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
56.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	912	3295
1	5002	2732

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes410.0ms

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	41	40
1	41	40

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4646×	body	1280	valid
1.4s	1891×	body	640	valid
270.0ms	572×	body	320	valid
267.0ms	196×	body	160	valid
93.0ms	695×	body	80	valid