Details

analyze2.8s (13.4%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample4.0s (19.5%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.3s	6305×	body	128	valid
749.0ms	803×	body	1024	valid
517.0ms	2376×	body	128	invalid
465.0ms	516×	body	1024	invalid
446.0ms	748×	body	512	valid
216.0ms	380×	body	512	invalid
163.0ms	391×	body	256	valid
62.0ms	161×	body	256	invalid
16.0ms	9×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1013×	`unsub-neg_binary64`
719×	`distribute-neg-out_binary64`
703×	`fma-def_binary64`
272×	`distribute-rgt-in_binary64`
229×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	35	24
2	83	24
3	312	24
4	1070	24
5	3549	24

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

Compiler

Compiled 95 to 55 computations (42.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.3s (6.1%)

Counts

4 → 180

Calls

4 calls:

792.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
443.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
21.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite63.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary64`
171×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	331	69
2	4470	69

Stop Event

1×	node limit

Counts

4 → 73

Calls

4 calls:

61.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
61.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
61.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
61.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify276.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

509×	`+-commutative_binary64`
461×	`fma-def_binary64`
405×	`associate-+r+_binary64`
141×	`associate-l_binary64`
85×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2196	44761

Stop Event

1×	node limit

Counts

253 → 281

prune1.3s (6.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	269	12	281
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	270	12	282

Error

1.6b

Counts

282 → 12

Alt Table

Status	Error	Program
	3.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	2.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	7.5b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	51.8b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	12.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
▶	1.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 1)) (-.f64 phi1 phi2)))
	38.2b	(-.f64 (fma.f64 R phi2 (/.f64 lambda2 (/.f64 phi1 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))))) (fma.f64 1/2 (/.f64 R (/.f64 phi1 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)))) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 lambda2 lambda2) (/.f64 phi1 (.f64 R (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))))))))
	41.7b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	1.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))) (-.f64 phi1 phi2)))
	55.2b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	23.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (sqrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 2)) (-.f64 phi1 phi2)))
	8.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))

Compiler

Compiled 60008 to 41195 computations (31.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
✓	0.4b	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 1)
✓	3.6b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series1.1s (5.1%)

Counts

4 → 96

Calls

4 calls:

358.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 1)
353.0ms	(exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
336.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
4.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

711×	`prod-diff_binary64`
253×	`fma-def_binary64`
180×	`log1p-udef_binary64`
179×	`expm1-udef_binary64`
170×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	214	41
2	2653	41

Stop Event

1×	node limit

Counts

4 → 139

Calls

4 calls:

55.0ms	(exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
55.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
55.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 1)
55.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
662×	`associate-/l*_binary64`
403×	`fma-def_binary64`
348×	`cancel-sign-sub-inv_binary64`
134×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2003
1	401	1979
2	1508	1831

Stop Event

1×	node limit

Counts

235 → 154

prune262.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Error

0.0b

Counts

166 → 8

Alt Table

Status	Error	Program
	38.2b	(-.f64 (fma.f64 R phi2 (/.f64 lambda2 (/.f64 phi1 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))))) (fma.f64 1/2 (/.f64 R (/.f64 phi1 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)))) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 lambda2 lambda2) (/.f64 phi1 (.f64 R (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))))))))
	41.7b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	1.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))) (-.f64 phi1 phi2)))
	55.2b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
▶	0.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))) 1)) (-.f64 phi1 phi2)))
	1.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (expm1.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))))) 1)) (-.f64 phi1 phi2)))
	3.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	1.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 1 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))) 1)) (-.f64 phi1 phi2)))

Compiler

Compiled 5603 to 3612 computations (35.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))
✓	0.2b	(exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))))
✓	0.4b	(log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))) 1)

series1.9s (9.1%)

Counts

4 → 96

Calls

4 calls:

638.0ms	(-.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))) 1)
629.0ms	(exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))))
617.0ms	(log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))
13.0ms	(.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))

rewrite70.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

305×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
167×	`expm1-log1p-u_binary64`
166×	`log1p-expm1-u_binary64`
162×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	110
1	352	46
2	4623	46

Stop Event

1×	node limit

Counts

4 → 136

Calls

4 calls:

68.0ms	(.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))
68.0ms	(exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))))
68.0ms	(log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))
68.0ms	(-.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2)))))) 1)

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
639×	`fma-def_binary64`
506×	`cancel-sign-sub-inv_binary64`
176×	`fma-neg_binary64`
163×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	3201
1	501	3069
2	1870	3000

Stop Event

1×	node limit

Counts

232 → 206

prune348.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	206	8	214

Error

0.0b

Counts

214 → 8

Alt Table

Status	Error	Program
	41.7b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	0.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2)))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2)))) 1)) (-.f64 phi1 phi2)))
	55.2b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
▶	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	38.2b	(-.f64 (fma.f64 R phi2 (/.f64 lambda2 (/.f64 phi1 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))))) (fma.f64 1/2 (/.f64 R (/.f64 phi1 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)))) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 lambda2 lambda2) (/.f64 phi1 (.f64 R (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))))))))
	1.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (pow.f64 (pow.f64 (+.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 1) 3) 1/3) 1)) (-.f64 phi1 phi2)))
	1.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (expm1.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))))) 1)) (-.f64 phi1 phi2)))
	3.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)

Compiler

Compiled 8056 to 5254 computations (34.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
✓	0.1b	(-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))))
✓	0.2b	(.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))

series2.1s (10.3%)

Counts

4 → 124

Calls

4 calls:

2.0s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
57.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))))
18.0ms	(-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))
12.0ms	(.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`add-sqr-sqrt_binary64`
230×	`log1p-expm1-u_binary64`
230×	`expm1-log1p-u_binary64`
227×	`add-cbrt-cube_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	125
1	467	65

Stop Event

1×	node limit

Counts

4 → 91

Calls

4 calls:

41.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
41.0ms	(-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))
41.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))))
41.0ms	(.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (*.f64 1/2 phi2)))

simplify413.0ms (2%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-def_binary64`
497×	`associate-+r+_binary64`
139×	`associate-/l*_binary64`
123×	`associate-l_binary64`
84×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2373	67211

Stop Event

1×	node limit

Counts

215 → 234

prune1.9s (9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	233	9	242

Error

0.0b

Counts

242 → 9

Alt Table

Status	Error	Program
	41.7b	(-.f64 (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	0.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2)))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2)))) 1)) (-.f64 phi1 phi2)))
	28.0b	(fma.f64 R phi2 (neg.f64 (*.f64 phi1 R)))
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	3.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	33.0b	(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (.f64 -2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2))))))))) (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) R))) (.f64 lambda2 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 R (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))))) (fma.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 R (sin.f64 (.f64 1/2 phi2)))))) (sqrt.f64 (/.f64 1 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (.f64 -2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2))))))))))) (.f64 (.f64 R lambda1) (sqrt.f64 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (.f64 -2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))))))
	38.2b	(-.f64 (fma.f64 R phi2 (/.f64 lambda2 (/.f64 phi1 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))))) (fma.f64 1/2 (/.f64 R (/.f64 phi1 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)))) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 lambda2 lambda2) (/.f64 phi1 (.f64 R (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))))))))
	1.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (pow.f64 (pow.f64 (+.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 1) 3) 1/3) 1)) (-.f64 phi1 phi2)))
	1.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (expm1.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))))) 1)) (-.f64 phi1 phi2)))

Compiler

Compiled 86269 to 65312 computations (24.3% saved)

regimes2.4s (11.7%)

Accuracy

Total 0.0b remaining (36.5%)

Threshold costs 0.0b (36.5%)

Counts

214 → 1

Compiler

Compiled 62676 to 45389 computations (27.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	36	45
2	54	45
3	64	45
4	70	45
5	71	45

Stop Event

1×

saturated

end303.0ms (1.5%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 681 to 511 computations (25% saved)

Details

analyze2.8s (13.4%)

sample4.0s (19.5%)

simplify22.0ms (0.1%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series1.3s (6.1%)

rewrite63.0ms (0.3%)

simplify276.0ms (1.3%)

prune1.3s (6.1%)

localize15.0ms (0.1%)

series1.1s (5.1%)

rewrite58.0ms (0.3%)

simplify45.0ms (0.2%)

prune262.0ms (1.3%)

localize23.0ms (0.1%)

series1.9s (9.1%)

rewrite70.0ms (0.3%)

simplify57.0ms (0.3%)

prune348.0ms (1.7%)

localize20.0ms (0.1%)

series2.1s (10.3%)

rewrite43.0ms (0.2%)

simplify413.0ms (2%)

prune1.9s (9%)

regimes2.4s (11.7%)

simplify3.0ms (0%)

end303.0ms (1.5%)

Profiling