Details

sample256.0ms

Algorithm

intervals

Results

175.0ms	140×	body	1280	valid
54.0ms	68×	body	640	valid
8.0ms	17×	body	320	valid
4.0ms	29×	body	80	valid
1.0ms	2×	body	160	valid

simplify9.0ms

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: 13.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.5b	(sin (- lambda1 lambda2))

rewrite30.0ms

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

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi1) (sin phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	443	1004
1	1340	773
2	5001	771

prune400.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite25.0ms

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

Counts

4 → 85

Calls

4 calls:

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
47.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	462	787
1	1582	631
2	5001	629

prune492.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 98

Calls

4 calls:

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

series317.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (cos lambda2))
51.0ms	(* (sin lambda1) (sin (- lambda2)))
45.0ms	(* (cos phi1) (sin phi2))
177.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	541	1025
1	2311	898
2	5001	897

prune637.0ms

Pruning

10 alts after pruning (10 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)
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

71×	`cos-mult`
60×	`frac-add`
59×	`sin-mult`
49×	`pow1`
35×	`associate-/r/`
34×	`frac-times` `associate-*r/`
31×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
19×	`pow-prod-down`
13×	`prod-exp` `cbrt-unprod`
10×	`cube-div`
9×	`associate-/l/`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-unpow`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `pow-pow` `flip3-+` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/r*`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `flip3--` `pow-plus` `unpow3` `cube-prod` `frac-sub` `flip--` `sub-div` `sqr-pow`
1×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `cube-neg` `sin-neg` `clear-num` `-commutative` `distribute-rgt-neg-out` `div-inv` `associate-/l`

Counts

4 → 159

Calls

4 calls:

49.0ms	(/ (* (* (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)
8.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
5.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series927.0ms

Counts

4 → 12

Calls

4 calls:

737.0ms	(/ (* (* (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)))))))
73.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
52.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
63.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify60.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1369	4349
1	5001	4080

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes398.0ms

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	57	138
1	57	138

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.1s	4624×	body	1280	valid
1.5s	1978×	body	640	valid
274.0ms	540×	body	320	valid
87.0ms	644×	body	80	valid
63.0ms	214×	body	160	valid