Details

sample253.0ms

Algorithm

intervals

Results

172.0ms	147×	body	1280	valid
52.0ms	79×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	3×	body	80	valid

simplify7.0ms

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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
44.0ms	(* (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)))))
24.0ms	(cos (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	264	773
1	1022	656
2	4705	656
3	5002	656

prune314.0ms

Filtered

69 candidates to 49 candidates (71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	13	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 2.2b

Counts

70 → 13

localize57.0ms

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)))))))

rewrite27.0ms

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:

9.0ms	(* (sin lambda1) (sin (- lambda2)))
8.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin (- lambda2)))
47.0ms	(* (sin phi1) (sin phi2))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
30.0ms	(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 (20.0ms)

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

prune459.0ms

Filtered

77 candidates to 55 candidates (71.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	61	16	77
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	74	16	90

Merged error: 2.0b

Counts

90 → 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))

rewrite14.0ms

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`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 67

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)
5.0ms	(pow (* (sin phi1) (sin phi2)) 3)
2.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
3.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series204.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
67.0ms	(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))

simplify192.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	297	1078
1	1032	937
2	4944	925
3	5001	925

prune472.0ms

Filtered

79 candidates to 52 candidates (65.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	81	14	95

Merged error: 2.0b

Counts

95 → 14

localize37.0ms

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))))))))

rewrite8.0ms

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

series382.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (sin (- lambda2)))
129.0ms	(cbrt (sin (- lambda2)))
111.0ms	(cbrt (sin (- lambda2)))
21.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin (- lambda2))) (cbrt (sin (- lambda2))))) (cbrt (sin (- lambda2))))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	165	639
1	404	565
2	1321	547
3	5001	518

prune346.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	53	14	67

Merged error: 2.0b

Counts

67 → 14

regimes564.0ms

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	27
1	34	27

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4753×	body	1280	valid
1.4s	2149×	body	640	valid
319.0ms	674×	body	320	valid
77.0ms	272×	body	160	valid
25.0ms	7×	body	2560	valid
22.0ms	148×	body	80	valid