Details

sample275.0ms

Algorithm

intervals

Results

199.0ms	157×	body	1280	valid
44.0ms	61×	body	640	valid
11.0ms	24×	body	320	valid
3.0ms	8×	body	160	valid
1.0ms	6×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.3b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b	(cos (- lambda1 lambda2))

rewrite13.0ms

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))

series121.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
50.0ms	(* (sin phi1) (sin phi2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

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

prune270.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.2b

localize38.0ms

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 lambda1) (sin (- lambda2)))
0.3b	(* (sin phi1) (sin phi2))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite16.0ms

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)
8.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
52.0ms	(* (sin lambda1) (sin (- lambda2)))
42.0ms	(* (sin phi1) (sin phi2))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify81.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (30.0ms)

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

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cbrt (sin lambda1)) (sin (- lambda2))))))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`acos-asin`

Counts

4 → 41

Calls

4 calls:

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

series312.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (sin lambda1))
93.0ms	(cbrt (sin lambda1))
108.0ms	(cbrt (sin lambda1))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cbrt (sin lambda1)) (sin (- lambda2))))))))

simplify168.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	150	521
1	345	457
2	1061	451
3	4574	448
4	5002	448

prune371.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))) R)
0.3b	(* (sin phi1) (sin phi2))
0.3b	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))
1.0b	(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative` `distribute-rgt-neg-out`
2×	`unswap-sqr`
1×	`acos-asin` `mul-1-neg` `sin-neg` `sin-mult`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))) R)
4.0ms	(* (sin phi1) (sin phi2))
25.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))
8.0ms	(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))) R)
46.0ms	(* (sin phi1) (sin phi2))
101.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))
16.0ms	(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

simplify139.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	299	1273
1	1134	1058
2	4834	1058
3	5002	1058

prune324.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.1b

regimes664.0ms

Accuracy

0% (0.3b 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	37	22
1	37	22

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.2s	4814×	body	1280	valid
1.5s	2068×	body	640	valid
326.0ms	644×	body	320	valid
120.0ms	327×	body	160	valid
32.0ms	141×	body	80	valid
28.0ms	9×	body	2560	valid