Details

analyze5.9s (20.1%)

Algorithm

1×

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

sample587.0ms (2%)

Algorithm

1×

intervals

Results

422.0ms	157×	body	1024	valid
66.0ms	46×	body	512	valid
45.0ms	8×	body	2048	valid
17.0ms	19×	body	256	valid
11.0ms	26×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
194×	`fma-neg_binary64`
83×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
47×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 108 to 55 computations (49.1% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	2.8b	(cos.f64 (-.f64 lambda1 lambda2))
✓	2.8b	(sin.f64 (-.f64 lambda1 lambda2))

series99.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

70.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
12.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
9.0ms	(sin.f64 (-.f64 lambda1 lambda2))
8.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`cos-sum_binary64`

Counts

4 → 90

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify160.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-neg_binary64`
422×	`associate-r_binary64`
380×	`associate-l_binary64`
380×	`distribute-rgt-neg-in_binary64`
340×	`distribute-lft-neg-in_binary64`

Counts

162 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	368	3902
1	782	3174
2	2633	2887
3	4652	2788
4	5011	2788

prune578.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	177	17	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	17	195

Error

5.6b

Counts

195 → 17

Alt Table

Status	Error	Program
	11.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.4b	(atan2.f64 (.f64 (log1p.f64 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cbrt.f64 (sin.f64 phi1)) (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.1b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.7b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (+.f64 (.f64 lambda2 (cos.f64 lambda1)) (.f64 1/2 (.f64 (sin.f64 lambda1) (pow.f64 lambda2 2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	31.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 phi1 (cos.f64 phi2)))))
	31.8b	(atan2.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	21.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	17.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))))))
	35.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.6b	(atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.9b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	20.2b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	39.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 8623 to 2334 computations (72.9% saved)

localize55.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	2.8b	(cos.f64 (-.f64 lambda1 lambda2))

series21.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

21.0ms

(*.f64 (cos.f64 phi1) (sin.f64 phi2))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

7.0ms

(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify124.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-neg_binary64`
480×	`distribute-rgt-neg-in_binary64`
423×	`distribute-lft-neg-in_binary64`
325×	`*-commutative_binary64`
265×	`associate-l_binary64`

Counts

44 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	572
1	191	512
2	572	487
3	1551	483
4	3033	483
5	4866	483
6	4975	483
7	4902	483

prune545.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	192	7	199
Fresh	12	4	16
Picked	1	0	1
Done	0	0	0
Total	205	11	216

Error

0.1b

Counts

216 → 11

Alt Table

Status	Error	Program
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.6b	(atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cbrt.f64 (sin.f64 phi1)) (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.1b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.8b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
	35.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (sin.f64 phi2))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.6b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 9150 to 2041 computations (77.7% saved)

localize55.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series154.0ms (0.5%)

Counts

2 → 56

Calls

2 calls:

136.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
18.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 50

Calls

2 calls:

14.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify166.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-r_binary64`
563×	`associate-l_binary64`
546×	`fma-neg_binary64`
385×	`distribute-rgt-neg-in_binary64`
300×	`*-commutative_binary64`

Counts

106 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	3509
1	965	3263
2	3764	3255
3	5052	3255

prune758.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	205	5	210
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	211	10	221

Error

0.1b

Counts

221 → 10

Alt Table

Status	Error	Program
	1.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	35.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 phi1)))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.6b	(atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))))))
	0.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) 3)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (sin.f64 phi2))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.6b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 11374 to 2327 computations (79.5% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1))
✓	0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda2))
✓	0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda1))
✓	29.4b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))

series28.0ms (0.1%)

Counts

4 → 60

Calls

4 calls:

14.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))
7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda1))
4.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda2))

rewrite42.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

23.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))
6.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda1))
4.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda2))

simplify151.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-neg_binary64`
464×	`fma-def_binary64`
415×	`*-commutative_binary64`
332×	`distribute-rgt-neg-in_binary64`
301×	`distribute-lft-neg-in_binary64`

Counts

165 → 179

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	195	1909
1	455	1574
2	1459	1482
3	3251	1416
4	4815	1408
5	4936	1408

prune711.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	178	11	189

Error

0.0b

Counts

189 → 11

Alt Table

Status	Error	Program
	1.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	35.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 phi1)))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.6b	(atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (.f64 (log.f64 (exp.f64 (pow.f64 (sin.f64 lambda1) 3))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))))))
✓	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2))))))))
	0.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) 3)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (sin.f64 phi2))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.6b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 10326 to 2236 computations (78.3% saved)

regimes2.4s (8.3%)

Accuracy

Total 0.1b remaining (54.7%)

Threshold costs 0.1b (54.7%)

Counts

178 → 1

Compiler

Compiled 47730 to 26986 computations (43.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
15×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	63
1	44	63
2	68	63
3	88	63
4	116	63
5	128	63
6	134	63
7	136	63
8	136	63

end1.0ms (0%)

Compiler: Compiled 42 to 24 computations (42.9% saved)

sample16.4s (56.3%)

Algorithm

1×

intervals

Results

12.1s	5324×	body	1024	valid
1.6s	1297×	body	512	valid
1.0s	190×	body	2048	valid
340.0ms	421×	body	256	valid
285.0ms	768×	body	128	valid

Compiler

Compiled 582 to 333 computations (42.8% saved)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Details

analyze5.9s (20.1%)

sample587.0ms (2%)

simplify59.0ms (0.2%)

prune6.0ms (0%)

localize41.0ms (0.1%)

series99.0ms (0.3%)

rewrite28.0ms (0.1%)

simplify160.0ms (0.6%)

prune578.0ms (2%)

localize55.0ms (0.2%)

series21.0ms (0.1%)

rewrite8.0ms (0%)

simplify124.0ms (0.4%)

prune545.0ms (1.9%)

localize55.0ms (0.2%)

series154.0ms (0.5%)

rewrite26.0ms (0.1%)

simplify166.0ms (0.6%)

prune758.0ms (2.6%)

localize33.0ms (0.1%)

series28.0ms (0.1%)

rewrite42.0ms (0.1%)

simplify151.0ms (0.5%)

prune711.0ms (2.4%)

regimes2.4s (8.3%)

simplify5.0ms (0%)

end1.0ms (0%)

sample16.4s (56.3%)

Profiling

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39