Details

sample246.0ms

Algorithm

intervals

Results

176.0ms	154×	body	1280	valid
41.0ms	66×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune8.0ms

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: 20.7b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b	(cos (- lambda1 lambda2))

rewrite21.0ms

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))

series182.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (* (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)))))
19.0ms	(cos (- lambda1 lambda2))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	300	873
1	1078	756
2	4807	756
3	5002	756

prune296.0ms

Filtered

82 candidates to 61 candidates (74.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	14	83

Merged error: 6.9b

Counts

83 → 14

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
2.1b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
39×	`associate-r` `associate-l`
30×	`pow1` `add-exp-log` `add-cbrt-cube`
21×	`unswap-sqr`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-commutative`
6×	`cos-mult`
4×	`add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin`

Counts

4 → 128

Calls

4 calls:

15.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
15.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
130.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	659	1909
1	3110	1632
2	5001	1632

prune566.0ms

Filtered

140 candidates to 91 candidates (65.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	128	12	140
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	141	13	154

Merged error: 6.8b

Counts

154 → 13

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
1.3b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
2.1b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`add-exp-log` `associate-l`
6×	`add-cbrt-cube`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff` `rem-log-exp`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

7.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
46.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
17.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (42.0ms)

Iter	Nodes	Cost
0	185	1853
1	408	1609
2	889	1605
3	1239	1605
4	3478	1601
5	5002	1601

prune363.0ms

Filtered

71 candidates to 49 candidates (69.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 6.7b

Counts

84 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))) R)
0.8b	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
1.4b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
24×	`associate-l`
21×	`associate-r`
18×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`unswap-sqr`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`cos-mult` `*-commutative` `difference-of-squares`
3×	`associate-*l/`
2×	`asin-acos` `flip3--` `times-frac` `flip--` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `diff-log` `associate-*r/` `associate--r-`

Counts

4 → 98

Calls

4 calls:

15.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
11.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))) R)
3.0ms	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
8.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
175.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))) R)
16.0ms	(asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
58.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	527	2162
1	2165	1948
2	5002	1948

prune455.0ms

Filtered

110 candidates to 75 candidates (68.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	108	16	124

Merged error: 6.4b

Counts

124 → 16

regimes636.0ms

Accuracy

0% (1.1b remaining)

Error of 4.5b against oracle of 3.5b and baseline of 4.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	68
1	40	68

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.6s	4695×	body	1280	valid
1.4s	2141×	body	640	valid
321.0ms	709×	body	320	valid
86.0ms	309×	body	160	valid
41.0ms	13×	body	2560	valid
25.0ms	135×	body	80	valid