Details

analyze3.8s (14.8%)

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)

sample475.0ms (1.8%)

Algorithm

1×

intervals

Results

237.0ms	172×	body	1024	valid
31.0ms	43×	body	512	valid
19.0ms	6×	body	2048	valid
6.0ms	11×	body	256	valid
5.0ms	24×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify30.0ms (0.1%)

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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	2.6b	(cos.f64 (-.f64 lambda1 lambda2))
✓	2.6b	(sin.f64 (-.f64 lambda1 lambda2))

series59.0ms (0.2%)

Counts

4 → 88

Calls

4 calls:

40.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms (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 → 89

Calls

4 calls:

6.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify146.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
437×	`associate-r_binary64`
403×	`associate-l_binary64`
392×	`distribute-rgt-neg-in_binary64`
354×	`distribute-lft-neg-in_binary64`

Counts

177 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	396	4016
1	844	3282
2	2780	3072
3	4739	2973
4	4994	2973
5	4918	2973

prune513.0ms (2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	174	19	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	19	194

Error

7.4b

Counts

194 → 19

Alt Table

Status	Error	Program
	41.8b	(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)))))))))
▶	7.7b	(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)))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	39.7b	(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 (sqrt.f64 lambda1) (sqrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (sin.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))))))))
	17.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	20.2b	(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 (.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 (sin.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))))))))
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	16.4b	(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)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
	19.9b	(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)))))
	23.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))
	34.8b	(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)))))
	38.8b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.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)))))
	26.3b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (.f64 (.f64 lambda1 lambda1) (-.f64 (.f64 1/2 (sin.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) 1/6) 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)))))
	20.0b	(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)))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	25.4b	(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)))))
	16.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))))))
	23.2b	(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 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))))))

Compiler

Compiled 8722 to 2429 computations (72.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	2.6b	(cos.f64 (-.f64 lambda1 lambda2))

series10.0ms (0%)

Counts

1 → 8

Calls

1 calls:

10.0ms

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

rewrite4.0ms (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))

simplify102.0ms (0.4%)

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

prune462.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	190	9	199
Fresh	15	3	18
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Error

0.1b

Counts

218 → 12

Alt Table

Status	Error	Program
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.8b	(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)))))
	8.3b	(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 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.7b	(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)))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	32.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (sin.f64 lambda1)) (.f64 (sqrt.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)))))
▶	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))))))
	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))))))
	7.7b	(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 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	7.7b	(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)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))

Compiler

Compiled 9266 to 2138 computations (76.9% 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 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

series118.0ms (0.5%)

Counts

3 → 104

Calls

3 calls:

55.0ms

(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

52.0ms

(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

10.0ms

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

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
29×	`pow1_binary64`
17×	`cbrt-unprod_binary64`
17×	`prod-exp_binary64`

Counts

3 → 75

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

7.0ms

(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

4.0ms

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

simplify113.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

835×	`associate-r_binary64`
696×	`associate-l_binary64`
609×	`fma-neg_binary64`
551×	`distribute-rgt-neg-in_binary64`
357×	`*-commutative_binary64`

Counts

179 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	342	4644
1	1038	4148
2	3853	4140
3	5453	4140

prune612.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	210	6	216
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	216	12	228

Error

0.0b

Counts

228 → 12

Alt Table

Status	Error	Program
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	28.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (sqrt.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))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	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))))))
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 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 (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))))))
▶	0.2b	(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 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
	29.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sqrt.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))))))
	8.3b	(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 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.7b	(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)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	2.6b	(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))))))

Compiler

Compiled 13122 to 2620 computations (80% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
	0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
✓	17.3b	(cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series5.5s (21.4%)

Counts

2 → 96

Calls

2 calls:

4.2s

(*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

1.4s

(cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`cbrt-div_binary64`
18×	`frac-times_binary64`
18×	`sin-cos-mult_binary64`
18×	`sin-mult_binary64`
12×	`associate-*r/_binary64`

Counts

2 → 62

Calls

2 calls:

11.0ms

(cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

9.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify164.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
535×	`cancel-sign-sub-inv_binary64`
386×	`fma-neg_binary64`
284×	`distribute-rgt-neg-in_binary64`
247×	`associate-r_binary64`

Counts

158 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	6789
1	712	6319
2	2195	5502
3	4853	5502
4	5012	5502

prune1.7s (6.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	599	0	599
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	599	12	611

Error

0.0b

Counts

611 → 12

Alt Table

Status	Error	Program
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	28.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (sqrt.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))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	16.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)))))
	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))))))
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 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 (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))))))
✓	0.2b	(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 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
	29.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sqrt.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))))))
	8.3b	(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 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.7b	(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)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	2.6b	(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))))))

Compiler

Compiled 51962 to 8115 computations (84.4% saved)

regimes1.7s (6.6%)

Accuracy

Total 0.1b remaining (50.8%)

Threshold costs 0.1b (50.8%)

Counts

183 → 1

Compiler

Compiled 50207 to 28172 computations (43.9% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

24×	`*-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	34	115
1	55	115
2	72	115
3	92	115
4	116	115
5	129	115
6	137	115
7	140	115
8	140	115

end1.0ms (0%)

Compiler: Compiled 73 to 33 computations (54.8% saved)

sample10.0s (38.8%)

Algorithm

1×

intervals

Results

7.4s	5367×	body	1024	valid
930.0ms	1257×	body	512	valid
587.0ms	175×	body	2048	valid
176.0ms	395×	body	256	valid
167.0ms	806×	body	128	valid

Compiler

Compiled 675 to 357 computations (47.1% 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

analyze3.8s (14.8%)

sample475.0ms (1.8%)

simplify30.0ms (0.1%)

prune3.0ms (0%)

localize21.0ms (0.1%)

series59.0ms (0.2%)

rewrite25.0ms (0.1%)

simplify146.0ms (0.6%)

prune513.0ms (2%)

localize26.0ms (0.1%)

series10.0ms (0%)

rewrite4.0ms (0%)

simplify102.0ms (0.4%)

prune462.0ms (1.8%)

localize30.0ms (0.1%)

series118.0ms (0.5%)

rewrite33.0ms (0.1%)

simplify113.0ms (0.4%)

prune612.0ms (2.4%)

localize33.0ms (0.1%)

series5.5s (21.4%)

rewrite26.0ms (0.1%)

simplify164.0ms (0.6%)

prune1.7s (6.7%)

regimes1.7s (6.6%)

simplify7.0ms (0%)

end1.0ms (0%)

sample10.0s (38.8%)

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