Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	105×	body	1280	valid
0.0hr	57×	body	640	valid
0.0hr	28×	body	320	valid
0.0hr	58×	body	80	valid
0.0hr	8×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

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

prune0.0hr

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.2b

Counts

2 → 1

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
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))))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite0.0hr

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` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

0.0hr	(* (sin theta) (sin delta))
0.0hr	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (sin theta) (sin delta))
0.0hr	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify0.0hr

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	289	930
1	894	837
2	3513	835
3	5002	835

prune0.0hr

Filtered

70 candidates to 51 candidates (27.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 0.1b

Counts

71 → 8

localize0.0hr

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))))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.7b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

0.0hr	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.0hr	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.0hr	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify0.0hr

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	253	1234
1	764	1106
2	2949	1102
3	5001	1102

prune0.0hr

Filtered

69 candidates to 51 candidates (26.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Merged error: 0.1b

Counts

77 → 9

localize0.0hr

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.4b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
17.0b	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`cbrt-prod` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult` `difference-of-squares` `sqr-pow`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow1/3` `diff-log` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.0hr	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.0hr	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0hr	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.0hr	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.0hr	(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify0.0hr

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	334	1587
1	1310	1468
2	5002	1463

prune0.0hr

Filtered

88 candidates to 62 candidates (29.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	88	9	97

Merged error: 0.0b

Counts

97 → 9

localize0.0hr

Local error

Found 4 expressions with local error:

0.3b	(pow (sin phi1) 3)
0.4b	(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
0.6b	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
17.0b	(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

0.0hr	(pow (sin phi1) 3)
0.0hr	(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
0.0hr	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
0.0hr	(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(pow (sin phi1) 3)
0.0hr	(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
0.0hr	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
0.0hr	(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

simplify0.0hr

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (0.0hr)

Iter	Nodes	Cost
0	459	1170
1	2011	1074
2	5002	1065

prune0.0hr

Filtered

88 candidates to 54 candidates (38.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	88	9	97

Merged error: 0.0b

Counts

97 → 9

regimes0.0hr

Accuracy

0% (0.1b remaining)

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

bsearch0.0hr

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	30	21
1	30	21

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	3116×	body	1280	valid
0.0hr	1827×	body	640	valid
0.0hr	728×	body	320	valid
0.0hr	2030×	body	80	valid
0.0hr	299×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling