Details

sample260.0ms

Algorithm

intervals

Results

172.0ms	147×	body	1280	valid
52.0ms	79×	body	640	valid
13.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`associate-l`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
5×	`unswap-sqr`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult`

Counts

4 → 70

Calls

4 calls:

9.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	300	873
1	1078	756
2	4831	756
3	5001	756

prune351.0ms

Filtered

82 candidates to 61 candidates (74.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Merged error: 2.2b

Counts

83 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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

series178.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (sin lambda2))
45.0ms	(* (sin phi1) (sin phi2))
69.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify74.0ms

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

prune411.0ms

Filtered

76 candidates to 51 candidates (67.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	60	16	76
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	73	16	89

Merged error: 2.0b

Counts

89 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(pow (* (sin phi1) (sin phi2)) 3)
0.7b	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
27.6b	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

3.0ms	(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
7.0ms	(pow (* (sin phi1) (sin phi2)) 3)
6.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
8.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series203.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
68.0ms	(pow (* (sin phi1) (sin phi2)) 3)
17.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
49.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	413	1336
1	1745	1175
2	5002	1169

prune493.0ms

Filtered

124 candidates to 61 candidates (49.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	126	14	140

Merged error: 2.0b

Counts

140 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

rewrite9.0ms

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:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (sin lambda2))
94.0ms	(cbrt (sin lambda2))
96.0ms	(cbrt (sin lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	138	507
1	324	445
2	863	439
3	3015	436
4	5001	436

prune305.0ms

Filtered

53 candidates to 42 candidates (79.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	53	14	67

Merged error: 2.0b

Counts

67 → 14

regimes507.0ms

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	34	24

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4753×	body	1280	valid
1.5s	2149×	body	640	valid
300.0ms	674×	body	320	valid
86.0ms	272×	body	160	valid
25.0ms	7×	body	2560	valid
23.0ms	148×	body	80	valid