Details

analyze2.6s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample291.0ms

Algorithm

intervals

Results

212.0ms	149×	body	1280	valid
52.0ms	67×	body	640	valid
8.0ms	15×	body	320	valid
4.0ms	12×	body	160	valid
2.0ms	13×	body	80	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.5b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.7b	(cos.f64 (-.f64 lambda1 lambda2))
1.7b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
25.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify69.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4969	586
1	4969	586

prune79.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 7.3b

Counts

71 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cos-diff_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `sin-cos-mult_binary64`
1×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 67

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
24.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify69.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4799	648
1	4799	648

prune76.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 0.1b

Counts

89 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
5×	`sin-cos-mult_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`sin-mult_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
26.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
31.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4944	952
1	4944	952

prune75.0ms

Filtered

59 candidates to 100 candidates (-69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 0.1b

Counts

110 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
3.4b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
3×	`log-prod_binary64` `log-pow_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
2×	`cos-mult_binary64` `unswap-sqr_binary64`
1×	`rem-log-exp_binary64` `associate-r/_binary64` `sin-mult_binary64` `exp-to-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `exp-prod_binary64`

Counts

4 → 77

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
29.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
12.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify57.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4956	732
1	4956	732

prune39.0ms

Filtered

57 candidates to 89 candidates (-56.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	88	12	100

Merged error: 0.1b

Counts

100 → 12

regimes443.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	139	46
1	139	46

end0.0ms

sample9.5s

Algorithm

intervals

Results

7.0s	4666×	body	1280	valid
1.7s	1969×	body	640	valid
305.0ms	535×	body	320	valid
99.0ms	612×	body	80	valid
87.0ms	218×	body	160	valid

Details

analyze2.6s

sample291.0ms

simplify18.0ms

prune11.0ms

localize27.0ms

rewrite23.0ms

series43.0ms

simplify69.0ms

prune79.0ms

localize36.0ms

rewrite23.0ms

series45.0ms

simplify69.0ms

prune76.0ms

localize34.0ms

rewrite31.0ms

series74.0ms

simplify52.0ms

prune75.0ms

localize37.0ms

rewrite25.0ms

series58.0ms

simplify57.0ms

prune39.0ms

regimes443.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample9.5s

Profiling