Details

sample269.0ms

Algorithm

intervals

Results

191.0ms	150×	body	1280	valid
39.0ms	54×	body	640	valid
11.0ms	28×	body	80	valid
7.0ms	15×	body	320	valid
3.0ms	9×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	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

localize27.0ms

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))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
28.0ms	(sin (- lambda1 lambda2))

simplify112.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	293	556
1	1064	489
2	4839	489
3	5001	489

prune321.0ms

Filtered

85 candidates to 63 candidates (74.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	74	11	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	11	86

Merged error: 5.4b

Counts

86 → 11

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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
33×	`associate-l`
20×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `associate-r`
10×	`unswap-sqr`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cos-diff` `associate-*l/`
2×	`cos-sum` `sin-cos-mult`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 91

Calls

4 calls:

19.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series311.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
45.0ms	(* (sin phi1) (cos phi2))
102.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	365	837
1	1473	741
2	5001	741

prune472.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Merged error: 0.1b

Counts

114 → 9

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))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate-l`
39×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
19×	`associate-r`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
11×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative` `sin-cos-mult`
4×	`distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 112

Calls

4 calls:

23.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin phi1) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
52.0ms	(* (sin phi1) (cos phi2))
50.0ms	(* (sin lambda1) (sin lambda2))
190.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify78.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	576	1256
1	2744	1127
2	5001	1127

prune751.0ms

Filtered

124 candidates to 82 candidates (66.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Merged error: 0.0b

Counts

133 → 13

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

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×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 76

Calls

4 calls:

6.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
2.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series431.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
102.0ms	(cbrt (sin lambda2))
102.0ms	(cbrt (sin lambda2))
103.0ms	(cbrt (sin lambda2))

simplify95.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	163	490
1	595	417
2	3517	375
3	5001	369

prune407.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 0.0b

Counts

101 → 12

regimes372.0ms

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	41	40
1	41	40

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.1s	4582×	body	1280	valid
1.5s	1964×	body	640	valid
267.0ms	549×	body	320	valid
93.0ms	688×	body	80	valid
70.0ms	217×	body	160	valid