Details

sample281.0ms

Algorithm

intervals

Results

213.0ms	162×	body	1280	valid
41.0ms	56×	body	640	valid
9.0ms	18×	body	320	valid
2.0ms	14×	body	80	valid
2.0ms	6×	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: 15.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite27.0ms

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))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series173.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify108.0ms

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

prune317.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite21.0ms

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` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series234.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sin phi1) (cos phi2))
88.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	316	541
1	1291	468
2	5002	468

prune410.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `flip--`

Counts

4 → 77

Calls

4 calls:

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

series346.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
91.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))
166.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	486	845
1	2349	739
2	5002	739

prune493.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (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	(pow (* (sin lambda1) (sin lambda2)) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cos-mult`
84×	`sin-mult`
50×	`associate-*r/` `frac-add` `associate-/r/`
49×	`pow1`
48×	`associate-*l/`
44×	`frac-times`
31×	`add-exp-log` `add-cbrt-cube`
27×	`frac-sub`
19×	`pow-prod-down`
15×	`sub-div`
13×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-/l/`
6×	`cube-div` `pow-unpow`
4×	`pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `sin-cos-mult` `add-log-exp` `rem-cube-cbrt`
3×	`cbrt-undiv` `flip3--` `flip3-+` `times-frac` `div-exp` `associate-/r*` `flip--` `flip-+`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `sqr-pow`
1×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 163

Calls

4 calls:

40.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
9.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series927.0ms

Counts

4 → 12

Calls

4 calls:

744.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
67.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
58.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
57.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify71.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1293	4502
1	5001	4261

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes391.0ms

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	46	77
1	46	77

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4608×	body	1280	valid
1.4s	1931×	body	640	valid
300.0ms	606×	body	320	valid
91.0ms	659×	body	80	valid
64.0ms	196×	body	160	valid