Details

analyze3.9s (17.8%)

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)

sample12.4s (56.5%)

Results

9.6s	5515×	body	1024	valid
1.4s	1344×	body	512	valid
768.0ms	172×	body	2048	valid
255.0ms	819×	body	128	valid
240.0ms	406×	body	256	valid

Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify33.0ms (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

prune3.0ms (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

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(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)

localize21.0ms (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)))
✓	4.2b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.4b	(sin.f64 (-.f64 lambda1 lambda2))

series57.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

37.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
12.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms (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:

6.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify122.0ms (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

prune411.0ms (1.9%)

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

6.4b

Counts

195 → 17

Alt Table

Status	Error	Program
	24.5b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.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)))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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))))))
	31.1b	(atan2.f64 (.f64 (sin.f64 (neg.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)))))
	13.1b	(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 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	27.3b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.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 (cos.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))))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.0b	(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))))))
	16.4b	(atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
	21.3b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.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)))))
	24.8b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (.f64 (+.f64 (.f64 -1/2 (.f64 lambda1 lambda1)) 1) (sin.f64 (neg.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)))))
	21.0b	(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)))))
	46.5b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.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)))))
	37.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.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)))))
▶	6.6b	(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)))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	44.5b	(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 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))))))))
	13.0b	(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)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	27.0b	(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)))))

Compiler

Compiled 8683 to 2372 computations (72.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	4.2b	(cos.f64 (-.f64 lambda1 lambda2))

series10.0ms (0%)

Counts

1 → 8

Calls

1 calls:

10.0ms

(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

rewrite5.0ms (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 → 21

Calls

1 calls:

3.0ms

(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-neg_binary64`
499×	`distribute-rgt-neg-in_binary64`
414×	`distribute-lft-neg-in_binary64`
325×	`*-commutative_binary64`
249×	`associate-l_binary64`

Counts

29 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	458
1	203	416
2	570	396
3	1526	373
4	2793	373
5	4861	373
6	4978	373
7	4997	373
8	4900	373

prune510.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	192	8	200
Fresh	13	3	16
Picked	1	0	1
Done	0	0	0
Total	206	11	217

Error

0.1b

Counts

217 → 11

Alt Table

Status	Error	Program
	20.9b	(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)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	37.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.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)))))
	6.6b	(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)) (log1p.f64 (expm1.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	6.6b	(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)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	6.6b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))) (cbrt.f64 (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)))))
	6.6b	(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))))))
	9.8b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda2)) (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)))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.7b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.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)))))
	13.1b	(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 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (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))))))

Compiler

Compiled 9192 to 2110 computations (77% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
✓	0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

series101.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

51.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
49.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cbrt-cube_binary64`
26×	`add-exp-log_binary64`
26×	`pow1_binary64`
16×	`cbrt-unprod_binary64`
16×	`prod-exp_binary64`

Counts

2 → 54

Calls

2 calls:

15.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
6.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-r_binary64`
617×	`associate-l_binary64`
505×	`fma-neg_binary64`
465×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`

Counts

150 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	4178
1	935	3724
2	3365	3718
3	5352	3718

prune798.0ms (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	263	7	270
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	269	12	281

Error

0.1b

Counts

281 → 12

Alt Table

Status	Error	Program
	3.4b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.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))))))
	20.9b	(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)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	37.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.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 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cos.f64 lambda2) (cbrt.f64 (sin.f64 lambda1)))) (.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))))))
	13.1b	(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 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (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 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))) (cbrt.f64 (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))))))
▶	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))) (log1p.f64 (expm1.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 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 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	6.6b	(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))))))
	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 (log.f64 (exp.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))))))

Compiler

Compiled 15839 to 3005 computations (81% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

prune832.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	271	11	282

Error

0.1b

Counts

282 → 11

Alt Table

Status	Error	Program
	3.4b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.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))))))
	37.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.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 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cos.f64 lambda2) (cbrt.f64 (sin.f64 lambda1)))) (.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))))))
	13.1b	(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 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (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 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)))) (.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))) (log1p.f64 (expm1.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 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 (.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))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2)))) (cbrt.f64 (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))))))
	6.6b	(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)) (log1p.f64 (expm1.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	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 (log.f64 (exp.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))))))

Compiler

Compiled 15768 to 2901 computations (81.6% saved)

regimes2.1s (9.5%)

Accuracy

Total 0.1b remaining (49.7%)

Threshold costs 0.1b (49.7%)

Counts

205 → 1

Compiler

Compiled 52861 to 30645 computations (42% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
14×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	77
1	47	77
2	64	77
3	84	77
4	108	77
5	121	77
6	129	77
7	132	77
8	132	77

end304.0ms (1.4%)

Compiler: Compiled 641 to 344 computations (46.3% 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

analyze3.9s (17.8%)

sample12.4s (56.5%)

simplify33.0ms (0.2%)

prune3.0ms (0%)

localize21.0ms (0.1%)

series57.0ms (0.3%)

rewrite27.0ms (0.1%)

simplify122.0ms (0.6%)

prune411.0ms (1.9%)

localize30.0ms (0.1%)

series10.0ms (0%)

rewrite5.0ms (0%)

simplify103.0ms (0.5%)

prune510.0ms (2.3%)

localize31.0ms (0.1%)

series101.0ms (0.5%)

rewrite26.0ms (0.1%)

simplify103.0ms (0.5%)

prune798.0ms (3.6%)

localize36.0ms (0.2%)

prune832.0ms (3.8%)

regimes2.1s (9.5%)

simplify6.0ms (0%)

end304.0ms (1.4%)

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