Details

sample262.0ms

Algorithm

intervals

Results

157.0ms	94×	body	1280	valid
58.0ms	63×	body	640	valid
13.0ms	21×	body	320	valid
11.0ms	67×	body	80	valid
4.0ms	11×	body	160	valid

simplify9.0ms

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

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: 0.2b

Counts

2 → 1

localize32.0ms

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))))))
0.5b	(- (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))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (sin phi1) (sin (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)))))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin theta) (sin delta))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
156.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify110.0ms

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

prune713.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

localize36.0ms

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))))))
0.5b	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.8b	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
13×	`log-pow`
11×	`pow1`
9×	`add-log-exp`
6×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `exp-prod` `exp-to-pow` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l` `associate--r+`
2×	`distribute-lft-out--`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
153.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
179.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
153.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify147.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	328	2628
1	957	1860
2	4945	1838
3	5001	1808

prune526.0ms

Filtered

100 candidates to 64 candidates (64.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	101	9	110

Merged error: 0.1b

Counts

110 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(pow (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
2.8b	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `log-pow` `add-cbrt-cube`
7×	`add-log-exp`
6×	`unpow-prod-down` `cube-prod` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod` `exp-prod` `exp-to-pow`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `rem-log-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(pow (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
3.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
152.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
233.0ms	(pow (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
151.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	257	1612
1	1067	1477
2	5001	1468

prune745.0ms

Filtered

101 candidates to 71 candidates (70.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Merged error: 0.0b

Counts

110 → 10

localize50.0ms

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	(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.4b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.5b	(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
21×	`unpow-prod-down` `cube-prod`
15×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`pow1`
8×	`pow-exp`
7×	`cube-mult` `unpow3` `sqr-pow`
6×	`pow-unpow`
5×	`cube-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `associate-l` `prod-exp` `rem-cube-cbrt`
2×	`pow-prod-down` `cbrt-unprod`
1×	`cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
6.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.0ms	(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series1.5s

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
920.0ms	(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
237.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
220.0ms	(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	387	2378
1	1733	2191
2	5003	2185

prune751.0ms

Filtered

131 candidates to 75 candidates (57.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Merged error: 0.0b

Counts

141 → 10

regimes429.0ms

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	40	58
1	40	58

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.1s	3102×	body	1280	valid
1.8s	1850×	body	640	valid
425.0ms	697×	body	320	valid
355.0ms	2057×	body	80	valid
114.0ms	294×	body	160	valid