Details

sample247.0ms

Algorithm

intervals

Results

179.0ms	156×	body	1280	valid
39.0ms	64×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	4×	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: 17.5b

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))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.5b	(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))

series121.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
44.0ms	(* (sin phi1) (sin phi2))
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
22.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

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

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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:

5.0ms	(* (sin lambda1) (sin lambda2))
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))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
45.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify77.0ms

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

prune378.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.4b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
25.9b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
2.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series175.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
65.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
48.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify185.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	297	619
1	1046	542
2	4843	542
3	5001	542

prune434.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.7b	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
24.4b	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
25.9b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-div` `cube-mult` `unpow-prod-down` `pow-unpow` `unpow3` `cube-prod` `sin-mult` `sqr-pow`
2×	`cbrt-div` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`
1×	`acos-asin` `pow-to-exp` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 67

Calls

4 calls:

3.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
2.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
2.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
2.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series175.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
19.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
45.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))
47.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify185.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	296	661
1	1024	597
2	4713	597
3	5001	597

prune419.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.1b

regimes418.0ms

Accuracy

0% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.7s	4828×	body	1280	valid
1.3s	2038×	body	640	valid
315.0ms	708×	body	320	valid
81.0ms	291×	body	160	valid
20.0ms	6×	body	2560	valid
19.0ms	130×	body	80	valid