Details

sample288.0ms

Algorithm

intervals

Results

187.0ms	107×	body	1280	valid
54.0ms	59×	body	640	valid
14.0ms	22×	body	320	valid
11.0ms	61×	body	80	valid
3.0ms	7×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune6.0ms

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: 0.1b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `sin-mult`

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (cos phi1) (sin delta))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos phi1) (sin delta))
161.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
189.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	295	931
1	976	838
2	3812	836
3	5002	836

prune372.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 0.1b

Counts

70 → 8

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.3b	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
18×	`add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down`
16×	`sin-mult`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`cos-mult`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-/l/`
6×	`frac-sub` `add-log-exp`
5×	`associate-r/` `associate-l/` `difference-of-squares`
4×	`pow-sqr` `pow-prod-up` `associate-/l*` `sub-div`
3×	`frac-times` `associate-/r*`
2×	`flip3--` `pow-plus` `associate-/r/` `flip--`
1×	`cbrt-undiv` `pow2` `sub-neg` `asin-acos` `sqr-cos` `frac-2neg` `flip3-+` `diff-log` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate--l+` `clear-num` `*-commutative` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
12.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
191.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
848.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
514.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	635	4481
1	3104	3982
2	5002	3958

prune731.0ms

Filtered

117 candidates to 84 candidates (71.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 0.0b

Counts

125 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
10×	`sin-mult`
8×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`cos-mult`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-sqr` `pow-prod-up`
3×	`associate-r/` `associate-l/` `frac-sub`
2×	`frac-times` `asin-acos` `pow-plus` `sub-div`
1×	`pow2` `sub-neg` `sqr-cos` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
8.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
189.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
530.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	427	2117
1	1980	1743
2	5001	1711

prune469.0ms

Filtered

84 candidates to 51 candidates (60.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.6b	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.9b	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod` `times-frac` `sin-mult`
10×	`cos-mult`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
6×	`unpow-prod-down` `cube-prod` `frac-sub` `add-log-exp`
5×	`pow1` `difference-of-squares`
4×	`associate-r/` `associate-l/` `associate-/l*` `sub-div`
3×	`pow-unpow` `associate-/r*`
2×	`cube-mult` `frac-times` `flip3--` `unpow3` `associate-/r/` `flip--` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `sqr-cos` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-sub` `div-exp` `pow-exp` `associate--l+` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

12.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))))
11.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
3.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
3.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

846.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))))
521.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
33.0ms	(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
7.0ms	(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	626	4558
1	3009	4040
2	5001	4010

prune750.0ms

Filtered

116 candidates to 81 candidates (69.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	116	8	124

Merged error: 0.0b

Counts

124 → 8

regimes387.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	56
1	48	56

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.6s	3149×	body	1280	valid
1.8s	1838×	body	640	valid
476.0ms	715×	body	320	valid
374.0ms	1975×	body	80	valid
135.0ms	323×	body	160	valid