Details

sample248.0ms

Algorithm

intervals

Results

165.0ms	147×	body	1280	valid
56.0ms	79×	body	640	valid
7.0ms	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	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: 15.1b

Counts

2 → 1

localize27.0ms

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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

17.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
6.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
10.0ms	(cos (- lambda1 lambda2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
48.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	424	1213
1	1306	1011
2	5001	1009

prune430.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	85	14	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	14	100

Merged error: 2.2b

Counts

100 → 14

localize32.0ms

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))))))

rewrite19.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

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)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (sin phi1) (sin phi2))
80.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify79.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	274	1015
1	872	860
2	2115	860
3	3356	860
4	5001	860

prune442.0ms

Filtered

84 candidates to 59 candidates (70.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	15	84
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	81	17	98

Merged error: 2.0b

Counts

98 → 17

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.7b	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite19.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (sin lambda2))
43.0ms	(* (sin phi1) (sin phi2))
81.0ms	(* (acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	273	1103
1	875	936
2	2104	936
3	3345	936
4	5001	936

prune493.0ms

Filtered

84 candidates to 59 candidates (70.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	85	16	101

Merged error: 2.0b

Counts

101 → 16

localize43.0ms

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 (+ (expm1 (log1p (* (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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`acos-asin`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
1.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (sin lambda2))
98.0ms	(cbrt (sin lambda2))
104.0ms	(cbrt (sin lambda2))
22.0ms	(acos (+ (expm1 (log1p (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

simplify108.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	149	605
1	363	539
2	1049	533
3	3444	530
4	5001	530

prune389.0ms

Filtered

61 candidates to 50 candidates (82.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	61	16	77

Merged error: 2.0b

Counts

77 → 16

regimes873.0ms

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

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

5.7s	4753×	body	1280	valid
1.5s	2149×	body	640	valid
289.0ms	674×	body	320	valid
76.0ms	272×	body	160	valid
24.0ms	7×	body	2560	valid
22.0ms	148×	body	80	valid