Details

sample260.0ms

Algorithm

intervals

Results

159.0ms	104×	body	1280	valid
46.0ms	53×	body	640	valid
16.0ms	60×	body	80	valid
14.0ms	24×	body	320	valid
6.0ms	15×	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

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(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))))
6.0ms	(* (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)))))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin theta) (sin delta))
7.0ms	(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))))))
190.0ms	(- (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

prune550.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	14	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	14	85

Merged error: 0.1b

Counts

85 → 14

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u`
3×	`fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`sub-neg` `asin-acos` `expm1-log1p` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `expm1-udef` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

1.0ms	(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))))
5.0ms	(* (sin phi1) (sin (log1p (expm1 (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)))))))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(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))))
169.0ms	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
186.0ms	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	291	1398
1	925	1241
2	4024	1235
3	5002	1229

prune548.0ms

Filtered

74 candidates to 58 candidates (78.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	75	13	88

Merged error: 0.0b

Counts

88 → 13

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
0.8b	(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`log-prod`
7×	`pow1`
6×	`add-exp-log` `prod-diff` `add-cbrt-cube` `add-log-exp`
5×	`exp-sum`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l`
2×	`sub-neg`
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 → 74

Calls

4 calls:

2.0ms	(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))))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
4.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
167.0ms	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
191.0ms	(- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
190.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	318	1858
1	988	1621
2	4055	1499
3	5001	1496

prune634.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	87	12	99

Merged error: 0.0b

Counts

99 → 12

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3))
0.4b	(pow (cos delta) 3)
0.4b	(pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

96×	`prod-diff`
61×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
49×	`add-cube-cbrt`
45×	`unpow-prod-down` `cube-prod`
29×	`sqr-pow`
23×	`cube-mult` `unpow3`
12×	`fma-neg`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
6×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-pow` `associate-r` `associate-l` `pow-exp` `rem-cube-cbrt`
2×	`pow-to-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
1×	`difference-cubes` `cube-div` `sub-neg` `flip3--` `diff-log` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
12.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3))
3.0ms	(pow (cos delta) 3)
5.0ms	(pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)

series913.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
470.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3))
29.0ms	(pow (cos delta) 3)
242.0ms	(pow (* (sin phi1) (sin (log1p (expm1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)

simplify184.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	773	7438
1	3655	5618
2	5001	5614

prune878.0ms

Filtered

215 candidates to 84 candidates (39.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	215	12	227

Merged error: 0.0b

Counts

227 → 12

regimes570.0ms

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	50	103
1	50	103

end0.0ms

sample8.7s

Algorithm

intervals

Results

5.5s	3152×	body	1280	valid
2.0s	1850×	body	640	valid
451.0ms	714×	body	320	valid
362.0ms	1992×	body	80	valid
124.0ms	292×	body	160	valid