Details

sample249.0ms

Algorithm

intervals

Results

143.0ms	94×	body	1280	valid
61.0ms	63×	body	640	valid
12.0ms	21×	body	320	valid
10.0ms	67×	body	80	valid
4.0ms	11×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
36×	`prod-diff`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
16×	`associate-l`
15×	`associate-r`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp` `unswap-sqr`
5×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 109

Calls

4 calls:

5.0ms	(* (sin theta) (sin delta))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin theta) (sin delta))
8.0ms	(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))))))
183.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	494	3725
1	1510	2512
2	5001	2414

prune516.0ms

Filtered

121 candidates to 70 candidates (57.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 0.1b

Counts

122 → 10

localize37.0ms

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))))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-pow`
53×	`add-sqr-sqrt`
51×	`prod-diff`
48×	`exp-prod`
44×	`*-un-lft-identity`
41×	`add-cube-cbrt`
15×	`associate-r` `associate-l`
11×	`pow1` `add-log-exp`
7×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube`
5×	`*-commutative` `unswap-sqr`
4×	`expm1-log1p-u` `exp-to-pow` `log1p-expm1-u`
3×	`fma-neg` `associate--r+`
2×	`diff-log` `rem-log-exp` `distribute-lft-out--`
1×	`sub-neg` `asin-acos` `flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `difference-of-squares`

Counts

4 → 134

Calls

4 calls:

3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
28.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
9.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(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))))))
184.0ms	(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
158.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	515	5351
1	1391	3577
2	5002	3313

prune579.0ms

Filtered

146 candidates to 74 candidates (50.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Merged error: 0.1b

Counts

156 → 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))))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

8.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
11.0ms	(pow (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
9.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
158.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
252.0ms	(pow (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)
156.0ms	(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	396	2242
1	1645	2080
2	5002	2050

prune882.0ms

Filtered

135 candidates to 86 candidates (63.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 0.0b

Counts

144 → 10

localize47.0ms

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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 236

Calls

4 calls:

8.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
20.0ms	(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
11.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
15.0ms	(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series1.7s

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0s	(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
249.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
238.0ms	(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify151.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	578	5046
1	2898	4649
2	5001	4579

prune967.0ms

Filtered

248 candidates to 97 candidates (39.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	248	10	258

Merged error: 0.0b

Counts

258 → 10

regimes450.0ms

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

5.2s	3102×	body	1280	valid
1.7s	1850×	body	640	valid
402.0ms	697×	body	320	valid
359.0ms	2057×	body	80	valid
123.0ms	294×	body	160	valid