Details

analyze3.0s (10.1%)

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
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)

sample4.1s (13.8%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.3s	6228×	body	128	valid
806.0ms	824×	body	1024	valid
532.0ms	2462×	body	128	invalid
478.0ms	780×	body	512	valid
418.0ms	443×	body	1024	invalid
213.0ms	370×	body	512	invalid
173.0ms	417×	body	256	valid
67.0ms	172×	body	256	invalid
11.0ms	7×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify127.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1413×	`unsub-neg_binary64`
897×	`distribute-neg-out_binary64`
703×	`fma-def_binary64`
583×	`neg-sub0_binary64`
478×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	35	24
2	83	24
3	224	24
4	658	24
5	2038	24
6	3128	24
7	3593	24
8	4399	24
9	4364	24
10	4430	24
11	4468	24
12	5035	24

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

3.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.8b	(.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%)

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)))
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.9s (6.4%)

Counts

4 → 180

Calls

4 calls:

1.3s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
583.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
23.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite72.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
307×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

4 → 77

Calls

4 calls:

70.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
70.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
70.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
70.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	331	69
2	4247	69
3	5102	69
0	0	0
1	0	0

simplify430.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1133×	`associate-r_binary64`
461×	`fma-def_binary64`
141×	`associate-l_binary64`
85×	`sub-neg_binary64`
65×	`associate-/l*_binary64`

Counts

257 → 273

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2196	44761
1	5035	44761

prune1.3s (4.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	257	16	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	16	274

Error

3.7b

Counts

274 → 16

Alt Table

Status	Error	Program
▶	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)) (-.f64 phi1 phi2)))
	54.0b	(-.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))))))
	9.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	36.4b	(cbrt.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	27.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3)))) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2) (.f64 1/8 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)))))) (-.f64 phi1 phi2)))
	5.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	8.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	45.3b	(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 R (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2)))) R)) (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))) 3))) (.f64 (.f64 lambda2 lambda2) (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 4) (.f64 lambda1 lambda1))))))))
	25.0b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (+.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))
	8.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	46.3b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda2 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))) (fma.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))) (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))))))
	51.1b	(.f64 lambda2 (.f64 R (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))))
	61.2b	(log.f64 (+.f64 1 (expm1.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	34.3b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	58.7b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))) (.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))))))) (+.f64 (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) lambda1)) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))))))

Compiler

Compiled 60498 to 41488 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) 2))))
✓	0.4b	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.1s (3.9%)

Counts

3 → 72

Calls

3 calls:

386.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)
379.0ms	(exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
372.0ms	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

rewrite111.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

706×	`prod-diff_binary64`
471×	`fma-udef_binary64`
283×	`fma-def_binary64`
231×	`fma-neg_binary64`
184×	`log1p-udef_binary64`

Counts

3 → 98

Calls

3 calls:

109.0ms	(exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
109.0ms	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
109.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	218	32
2	2593	32
3	4699	32
4	4727	32
5	4935	32
0	0	0
1	0	0

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

170 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1633
1	394	1613
2	1430	1478
3	5231	1478

prune471.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	181	17	198

Error

3.6b

Counts

198 → 17

Alt Table

Status	Error	Program
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))) 1)) (-.f64 phi1 phi2)))
	9.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi1)))) 1)) (-.f64 phi1 phi2)))
▶	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	26.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (-.f64 (fma.f64 1/48 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (pow.f64 phi2 3)) (log1p.f64 (cos.f64 (.f64 1/2 phi1)))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (+.f64 (fma.f64 1/16 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3))) (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) 2)) (.f64 1/24 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 3) (pow.f64 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) phi2) 3)))) (.f64 1/8 (.f64 (.f64 phi2 phi2) (+.f64 (/.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (cos.f64 (.f64 1/2 phi1)) 1)) (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)))))))))) 1)) (-.f64 phi1 phi2)))
	54.0b	(-.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))))))
	29.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	45.3b	(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 R (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2)))) R)) (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))) 3))) (.f64 (.f64 lambda2 lambda2) (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 4) (.f64 lambda1 lambda1))))))))
	4.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cbrt.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)) (pow.f64 (cbrt.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)) 2) -1)) (-.f64 phi1 phi2)))
	8.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	8.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	51.1b	(.f64 lambda2 (.f64 R (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))))
	36.4b	(cbrt.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	61.2b	(log.f64 (+.f64 1 (expm1.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	34.3b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	5.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	26.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1) (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) -1))) (-.f64 phi1 phi2)))
	58.7b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 R (.f64 phi2 phi2)) (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (fma.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))) (.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))))))) (+.f64 (/.f64 (.f64 phi1 (.f64 R phi2)) (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) lambda1)) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))))))

Compiler

Compiled 7200 to 4569 computations (36.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.6b	(expm1.f64 (*.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))
✓	0.6b	(+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series519.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

514.0ms	(expm1.f64 (*.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))
5.0ms	(+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)

rewrite57.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

636×	`prod-diff_binary64`
227×	`log1p-udef_binary64`
226×	`expm1-udef_binary64`
129×	`add-sqr-sqrt_binary64`
127×	`expm1-log1p-u_binary64`

Counts

2 → 56

Calls

2 calls:

56.0ms	(expm1.f64 (*.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))
56.0ms	(+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	271	28
2	3125	28
3	4938	28
0	0	0
1	0	0

simplify95.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

391×	`fma-def_binary64`
365×	`associate-r_binary64`
356×	`associate-+r+_binary64`
245×	`associate-/l*_binary64`
243×	`+-commutative_binary64`

Counts

104 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	3675
1	1068	3609
2	4854	3601
3	4984	3601

prune785.0ms (2.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	269	4	273
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	274	16	290

Error

3.6b

Counts

290 → 16

Alt Table

Status	Error	Program
	10.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	54.0b	(-.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))))))
	45.3b	(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 R (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2)))) R)) (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))) 3))) (.f64 (.f64 lambda2 lambda2) (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 4) (.f64 lambda1 lambda1))))))))
	8.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi2))) 1))))) (-.f64 phi1 phi2)))
	10.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi1))) 2) (+.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	26.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (-.f64 (fma.f64 1/48 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (pow.f64 phi2 3)) (log1p.f64 (cos.f64 (.f64 1/2 phi1)))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (+.f64 (fma.f64 1/16 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3))) (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) 2)) (.f64 1/24 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 3) (pow.f64 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) phi2) 3)))) (.f64 1/8 (.f64 (.f64 phi2 phi2) (+.f64 (/.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (cos.f64 (.f64 1/2 phi1)) 1)) (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)))))))))) 1)) (-.f64 phi1 phi2)))
	29.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	9.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi1)))) 1)) (-.f64 phi1 phi2)))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 (sqrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	8.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	51.1b	(.f64 lambda2 (.f64 R (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))))
	36.4b	(cbrt.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	61.2b	(log.f64 (+.f64 1 (expm1.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	34.3b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
▶	5.0b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	26.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1) (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) -1))) (-.f64 phi1 phi2)))

Compiler

Compiled 19623 to 13794 computations (29.7% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
✓	1.3b	(cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))
	3.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series9.6s (32.6%)

Counts

3 → 168

Calls

3 calls:

5.7s

(pow.f64 (cbrt.f64 (*.f64 R (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)

3.8s

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

22.0ms

(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))

rewrite81.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

333×	`log1p-udef_binary64`
186×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
175×	`add-log-exp_binary64`

Counts

3 → 82

Calls

3 calls:

78.0ms

(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))

78.0ms

(pow.f64 (cbrt.f64 (*.f64 R (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)

78.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	65
1	378	65
2	4647	65
3	5075	65
0	0	0
1	0	0

simplify538.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
159×	`associate-/l*_binary64`
145×	`associate-*r/_binary64`
99×	`sub-neg_binary64`
69×	`sqr-pow_binary64`

Counts

250 → 291

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3097	61449
1	5018	61449

prune1.6s (5.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	318	5	323
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	322	17	339

Error

3.5b

Counts

339 → 17

Alt Table

Status	Error	Program
	45.3b	(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 R (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2)))) R)) (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (+.f64 (.f64 phi1 phi1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) (.f64 2 (.f64 phi1 phi2))) 3))) (.f64 (.f64 lambda2 lambda2) (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 4) (.f64 lambda1 lambda1))))))))
	4.3b	(.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) (.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) R))
	8.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi2))) 1))))) (-.f64 phi1 phi2)))
	16.6b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))) 3)
	9.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi1)))) 1)) (-.f64 phi1 phi2)))
	5.3b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))) 2) (.f64 (cbrt.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))) (pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)))
	10.5b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 1/2 phi1)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	4.9b	(.f64 (cbrt.f64 R) (.f64 (cbrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) (pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)))
	8.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	10.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (cos.f64 (*.f64 1/2 phi1))) 2) (+.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	26.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (-.f64 (fma.f64 1/48 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (pow.f64 phi2 3)) (log1p.f64 (cos.f64 (.f64 1/2 phi1)))) (fma.f64 1/2 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) (+.f64 (fma.f64 1/16 (/.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3))) (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) 2)) (.f64 1/24 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 3) (pow.f64 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) 1) phi2) 3)))) (.f64 1/8 (.f64 (.f64 phi2 phi2) (+.f64 (/.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (cos.f64 (.f64 1/2 phi1)) 1)) (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) (tan.f64 (/.f64 (*.f64 1/2 phi1) 2)))))))))) 1)) (-.f64 phi1 phi2)))
	10.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	29.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1) 2) (+.f64 (+.f64 (sqrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) 1) 1))))) (-.f64 phi1 phi2)))
	36.4b	(cbrt.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	61.2b	(log.f64 (+.f64 1 (expm1.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	26.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1) (+.f64 (hypot.f64 1 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) -1))) (-.f64 phi1 phi2)))

Compiler

Compiled 81273 to 56554 computations (30.4% saved)

regimes3.0s (10.3%)

Accuracy

Total 0.4b remaining (10%)

Threshold costs 0.4b (10%)

Counts

258 → 1

Compiler

Compiled 80379 to 56963 computations (29.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	34	24
3	38	24
4	40	24
5	39	24

end481.0ms (1.6%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 1024 to 707 computations (31% saved)

Details

analyze3.0s (10.1%)

sample4.1s (13.8%)

simplify127.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0%)

series1.9s (6.4%)

rewrite72.0ms (0.2%)

simplify430.0ms (1.5%)

prune1.3s (4.4%)

localize15.0ms (0.1%)

series1.1s (3.9%)

rewrite111.0ms (0.4%)

simplify51.0ms (0.2%)

prune471.0ms (1.6%)

localize22.0ms (0.1%)

series519.0ms (1.8%)

rewrite57.0ms (0.2%)

simplify95.0ms (0.3%)

prune785.0ms (2.7%)

localize15.0ms (0%)

series9.6s (32.6%)

rewrite81.0ms (0.3%)

simplify538.0ms (1.8%)

prune1.6s (5.3%)

regimes3.0s (10.3%)

simplify3.0ms (0%)

end481.0ms (1.6%)

Profiling