Details

sample278.0ms

Algorithm

intervals

Results

175.0ms	107×	body	1280	valid
52.0ms	59×	body	640	valid
18.0ms	22×	body	320	valid
10.0ms	61×	body	80	valid
3.0ms	7×	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: 0.1b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (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))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite22.0ms

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

Counts

4 → 71

Calls

4 calls:

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

series388.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos phi1) (sin delta))
155.0ms	(* (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))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	329	1199
1	1108	1065
2	4447	1059
3	5001	1054

prune458.0ms

Filtered

83 candidates to 65 candidates (78.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 0.1b

Counts

84 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (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))))
0.6b	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
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`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `sin-mult` `distribute-lft-out--` `expm1-udef` `associate--r-` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (cos phi1) (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))))
9.0ms	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos phi1) (sin delta))
153.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
222.0ms	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	369	1973
1	1240	1353
2	5002	1343

prune495.0ms

Filtered

92 candidates to 66 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.4b	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `pow2` `asin-acos` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
6.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
791.0ms	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
144.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
489.0ms	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	407	3418
1	1583	2987
2	5001	2850

prune632.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	90	8	98

Merged error: 0.0b

Counts

98 → 8

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.4b	(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)
0.6b	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
2.0ms	(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)
1.0ms	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
775.0ms	(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
146.0ms	(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2)
361.0ms	(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	399	2191
1	1546	1982
2	5001	1961

prune512.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	81	8	89

Merged error: 0.0b

Counts

89 → 8

regimes364.0ms

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	43	38
1	45	38
2	45	38

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.2s	3149×	body	1280	valid
1.8s	1838×	body	640	valid
447.0ms	715×	body	320	valid
346.0ms	1975×	body	80	valid
136.0ms	323×	body	160	valid