Details

sample277.0ms

Algorithm

intervals

Results

206.0ms	163×	body	1280	valid
42.0ms	60×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	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: 16.9b

Counts

2 → 1

localize23.0ms

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)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.7b	(cos (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

8.0ms	(* (* (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)))))
5.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms	(* (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))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	1113
1	1250	911
2	5001	909

prune376.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	70	16	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	16	87

Merged error: 2.8b

Counts

87 → 16

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `cos-mult`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

9.0ms	(* (* (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)
9.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* (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)
108.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	434	1553
1	1716	1275
2	5001	1274

prune537.0ms

Filtered

96 candidates to 57 candidates (59.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	77	19	96
Fresh	14	1	15
Picked	1	0	1
Done	0	0	0
Total	92	20	112

Merged error: 2.7b

Counts

112 → 20

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin 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)
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`associate-l` `cos-mult`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `-commutative`
1×	`acos-asin` `frac-times` `associate-*r/` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

15.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
17.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
107.0ms	(* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2))))) R)
33.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (* (cos phi1) (cos phi2)) (sin lambda1)) (sin lambda2)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	434	1512
1	1817	1249
2	5002	1248

prune499.0ms

Filtered

93 candidates to 56 candidates (60.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	10	9	19
Picked	1	0	1
Done	0	0	0
Total	95	18	113

Merged error: 2.7b

Counts

113 → 18

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`acos-asin` `log-prod`
2×	`exp-diff` `cos-mult` `sin-mult`
1×	`frac-times` `log-div` `associate-r/` `rem-log-exp` `associate-r` `associate-l` `associate-l/` `*-commutative` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

9.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
42.0ms	(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))))))))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify132.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	286	1600
1	920	1378
2	4259	1378
3	5001	1378

prune388.0ms

Filtered

81 candidates to 53 candidates (65.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	82	17	99

Merged error: 2.7b

Counts

99 → 17

regimes885.0ms

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample8.0s

Algorithm

intervals

Results

5.8s	4788×	body	1280	valid
1.4s	2121×	body	640	valid
297.0ms	673×	body	320	valid
77.0ms	279×	body	160	valid
42.0ms	12×	body	2560	valid
19.0ms	127×	body	80	valid