Details

sample281.0ms

Algorithm

intervals

Results

194.0ms	113×	body	1280	valid
40.0ms	42×	body	640	valid
13.0ms	22×	body	320	valid
12.0ms	68×	body	80	valid
4.0ms	11×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	22
1	61	22
2	71	22
3	72	22
4	72	22

prune5.0ms

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: 0.2b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* (sin theta) (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)))))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin theta) (sin delta))
148.0ms	(* (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))))
175.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	322	1198
1	1021	1064
2	4124	1059
3	5001	1054

prune509.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	68	16	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	16	85

Merged error: 0.1b

Counts

85 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`sub-neg` `asin-acos` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

1.0ms	(log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms	(* (sin phi1) (sin (log1p (expm1 (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 (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
156.0ms	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
170.0ms	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify115.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	289	1386
1	895	1231
2	3906	1225
3	5001	1219

prune433.0ms

Filtered

74 candidates to 57 candidates (77.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	74	16	90

Merged error: 0.1b

Counts

90 → 16

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* (sin theta) (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)))))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
153.0ms	(* (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))))
178.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	322	1198
1	1021	1064
2	4124	1059
3	5001	1054

prune512.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	84	16	100

Merged error: 0.1b

Counts

100 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* (sin theta) (sin delta))
6.0ms	(* (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)))))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin theta) (sin delta))
154.0ms	(* (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))))
175.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	322	1198
1	1021	1064
2	4124	1059
3	5001	1054

prune419.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	84	16	100

Merged error: 0.1b

Counts

100 → 16

regimes570.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.2s	3117×	body	1280	valid
1.8s	1830×	body	640	valid
455.0ms	735×	body	320	valid
373.0ms	2002×	body	80	valid
135.0ms	316×	body	160	valid

Details

sample281.0ms

simplify10.0ms

prune5.0ms

localize31.0ms

rewrite17.0ms

series372.0ms

simplify107.0ms

prune509.0ms

localize35.0ms

rewrite13.0ms

series373.0ms

simplify115.0ms

prune433.0ms

localize39.0ms

rewrite17.0ms

series381.0ms

simplify107.0ms

prune512.0ms

localize35.0ms

rewrite18.0ms

series383.0ms

simplify105.0ms

prune419.0ms

regimes570.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.2s

Profiling