Details

sample274.0ms

Algorithm

intervals

Results

193.0ms	157×	body	1280	valid
43.0ms	68×	body	640	valid
7.0ms	12×	body	160	valid
7.0ms	15×	body	320	valid
6.0ms	1×	body	2560	valid
1.0ms	3×	body	80	valid

simplify6.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize28.0ms

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))

series114.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
46.0ms	(* (sin phi1) (sin phi2))
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

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

prune285.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize35.0ms

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)))))))

rewrite15.0ms

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` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

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))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series179.0ms

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)
42.0ms	(* (sin phi1) (sin phi2))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	281	1000
1	916	859
2	2499	835
3	5001	835

prune426.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize37.0ms

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)))))))

rewrite13.0ms

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` `sin-neg` `log-pow` `distribute-rgt-neg-out`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (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)))))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (sin phi2))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
52.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	244	884
1	734	761
2	2037	737
3	5001	737

prune477.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.7b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
0.7b	(log (log (exp (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)))))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`log-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity` `log-pow`
7×	`pow1`
5×	`add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`acos-asin`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

1.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
2.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.0ms	(log (log (exp (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)))))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
48.0ms	(log (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	151	1583
1	277	1371
2	569	1323
3	1009	1323
4	1621	1323
5	2620	1323
6	5001	1323

prune303.0ms

Filtered

64 candidates to 40 candidates (62.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.3b

regimes1.1s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	29
1	34	29

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.7s	4807×	body	1280	valid
1.4s	2090×	body	640	valid
290.0ms	660×	body	320	valid
90.0ms	301×	body	160	valid
53.0ms	16×	body	2560	valid
20.0ms	129×	body	80	valid