Details

sample265.0ms

Algorithm

intervals

Results

197.0ms	150×	body	1280	valid
38.0ms	54×	body	640	valid
7.0ms	15×	body	320	valid
4.0ms	28×	body	80	valid
3.0ms	9×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

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: 11.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-l` `prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sub-neg` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff`

Counts

4 → 99

Calls

4 calls:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- lambda1 lambda2))

series205.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	449	1132
1	1334	897
2	5001	871

prune624.0ms

Filtered

111 candidates to 75 candidates (67.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	13	112

Merged error: 5.4b

Counts

112 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(cos (- lambda1 lambda2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `associate-l`
26×	`*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`cos-sum`
9×	`prod-diff`
6×	`unswap-sqr`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cos-diff` `associate-*l/`
2×	`sin-cos-mult`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 104

Calls

4 calls:

19.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
5.0ms	(* (sin phi1) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms	(cos (- lambda1 lambda2))

series297.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
47.0ms	(* (sin phi1) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	492	1125
1	1840	942
2	5001	938

prune541.0ms

Filtered

116 candidates to 82 candidates (70.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	7	116
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 0.1b

Counts

129 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

288×	`prod-diff`
279×	`add-sqr-sqrt`
180×	`associate-l`
174×	`*-un-lft-identity`
167×	`associate-r`
158×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
59×	`unswap-sqr`
53×	`*-commutative`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `cos-mult` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-*l/`
2×	`sub-neg` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 411

Calls

4 calls:

19.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
5.0ms	(* (sin phi1) (cos phi2))
8.0ms	(* (sin lambda1) (sin (- lambda2)))
36.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
48.0ms	(* (sin phi1) (cos phi2))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
193.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1763	13233
1	5002	9578

prune902.0ms

Filtered

423 candidates to 125 candidates (29.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	413	10	423
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	420	13	433

Merged error: 0.0b

Counts

433 → 13

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))
0.3b	(* (cbrt (cos lambda1)) (cbrt (cos lambda1)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))
6.0ms	(* (cbrt (cos lambda1)) (cbrt (cos lambda1)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (cos lambda1))
99.0ms	(cbrt (cos lambda1))
105.0ms	(cbrt (cos lambda1))
161.0ms	(* (cbrt (cos lambda1)) (cbrt (cos lambda1)))

simplify108.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	137	508
1	544	435
2	3667	393
3	5001	387

prune573.0ms

Filtered

96 candidates to 68 candidates (70.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	96	13	109

Merged error: 0.0b

Counts

109 → 13

regimes518.0ms

Accuracy

0% (0.2b 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	52	45
1	54	45
2	54	45

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.1s	4582×	body	1280	valid
1.5s	1964×	body	640	valid
260.0ms	549×	body	320	valid
101.0ms	688×	body	80	valid
72.0ms	217×	body	160	valid