Details

sample253.0ms

Algorithm

intervals

Results

181.0ms	157×	body	1280	valid
42.0ms	68×	body	640	valid
6.0ms	15×	body	320	valid
4.0ms	1×	body	2560	valid
3.0ms	12×	body	160	valid
0.0ms	3×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.3b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 55

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series118.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
47.0ms	(* (sin phi1) (sin phi2))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	200	661
1	565	569
2	1790	569
3	5001	569

prune320.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (sin lambda1) (sin lambda2))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms	(* (sin phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
43.0ms	(* (sin phi1) (sin phi2))
46.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	929
1	831	774
2	1930	774
3	3056	774
4	5001	774

prune402.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (sin lambda1) (sin lambda2))
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`log-prod`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`acos-asin` `rem-log-exp` `log-pow`

Counts

4 → 58

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin phi1) (sin phi2))
48.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify124.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	223	819
1	649	681
2	1484	681
3	2358	681
4	4932	681
5	5002	681

prune466.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (sin lambda1) (sin lambda2))
1.2b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.8b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`acos-asin` `exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
1.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin phi1) (sin phi2))
45.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
48.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	226	561
1	643	477
2	1467	477
3	2553	477
4	5002	477

prune370.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 3.4b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	19
1	32	19

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.7s	4807×	body	1280	valid
1.4s	2090×	body	640	valid
293.0ms	660×	body	320	valid
229.0ms	301×	body	160	valid
62.0ms	16×	body	2560	valid
19.0ms	129×	body	80	valid