Details

analyze2.9s (11.1%)

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)

sample4.8s (18.7%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

2.0s	6232×	body	128	valid
754.0ms	779×	body	1024	valid
604.0ms	2533×	body	128	invalid
457.0ms	457×	body	1024	invalid
455.0ms	761×	body	512	valid
235.0ms	389×	body	512	invalid
210.0ms	473×	body	256	valid
74.0ms	163×	body	256	invalid
21.0ms	11×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify128.0ms (0.5%)

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

2.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.8b	(.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)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))
✓	4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.0s (7.8%)

Counts

3 → 132

Calls

3 calls:

2.0s

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

26.0ms

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

5.0ms

(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`associate-l_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 53

Calls

3 calls:

8.0ms

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

3.0ms

(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

3.0ms

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

simplify328.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

868×	`*-commutative_binary64`
674×	`associate-r_binary64`
279×	`+-commutative_binary64`
255×	`fma-def_binary64`
228×	`times-frac_binary64`

Counts

185 → 219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1391	25367
1	4721	25194
2	5116	25194

prune812.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	205	14	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	14	220

Error

2.6b

Counts

220 → 14

Alt Table

Status	Error	Program
	24.8b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	41.4b	(-.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))))))
▶	3.2b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	30.8b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	54.4b	(-.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))))))
	32.9b	(.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	9.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	4.0b	(.f64 (.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (cbrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	47.7b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 phi1 phi1) R) (.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) lambda2)) (fma.f64 1/2 (/.f64 (.f64 (.f64 phi2 phi2) R) (.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) lambda2)) (.f64 lambda2 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) R)))) (fma.f64 R (.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) lambda1) (/.f64 (.f64 phi1 (.f64 phi2 R)) (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda2))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	36.0b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	39.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2))) phi1)))))
	46.2b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))

Compiler

Compiled 33516 to 22313 computations (33.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.3b	(.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
✓	0.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series5.4s (20.8%)

Counts

2 → 88

Calls

2 calls:

3.4s

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

2.0s

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

5.0ms

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

4.0ms

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

simplify396.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

981×	`associate-r_binary64`
422×	`fma-def_binary64`
372×	`associate-+r+_binary64`
163×	`associate-l_binary64`
59×	`sqr-pow_binary64`

Counts

135 → 178

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1971	45762
1	5443	45762

prune1.3s (5.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	361	5	366
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	367	13	380

Error

2.6b

Counts

380 → 13

Alt Table

Status	Error	Program
	3.2b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
	30.8b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	54.4b	(-.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))))))
	3.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	9.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	35.0b	(.f64 (exp.f64 (log.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	39.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2))) phi1)))))
	41.4b	(-.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))))))
	46.2b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	9.7b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2))))
▶	3.2b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
	33.2b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))

Compiler

Compiled 69259 to 45971 computations (33.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
✓	0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
	4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
✓	4.1b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series1.9s (7.4%)

Counts

3 → 108

Calls

3 calls:

1.9s

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

5.0ms

(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))

5.0ms

(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

3 → 49

Calls

3 calls:

5.0ms

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

4.0ms

(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))

3.0ms

(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

simplify316.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

829×	`*-commutative_binary64`
649×	`associate-r_binary64`
260×	`+-commutative_binary64`
235×	`fma-def_binary64`
218×	`times-frac_binary64`

Counts

157 → 178

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1341	24654
1	4489	24478
2	5072	24478

prune653.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	210	12	222

Error

2.6b

Counts

222 → 12

Alt Table

Status	Error	Program
▶	3.2b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
	30.8b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	54.4b	(-.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))))))
	3.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	9.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	35.0b	(.f64 (exp.f64 (log.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	39.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2))) phi1)))))
	41.4b	(-.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))))))
	46.2b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	9.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))

Compiler

Compiled 35013 to 23100 computations (34% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
✓	0.4b	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))
	4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	4.1b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series1.9s (7.3%)

Counts

2 → 84

Calls

2 calls:

1.9s

(*.f64 (*.f64 R (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))

15.0ms

(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms

(*.f64 (*.f64 R (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))

0.0ms

(expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))

simplify299.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

853×	`*-commutative_binary64`
671×	`associate-r_binary64`
276×	`+-commutative_binary64`
244×	`fma-def_binary64`
218×	`times-frac_binary64`

Counts

118 → 163

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1367	24469
1	4619	24308
2	4988	24308

prune672.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	223	12	235

Error

2.6b

Counts

235 → 12

Alt Table

Status	Error	Program
✓	3.2b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log1p.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2))))
	30.8b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	54.4b	(-.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))))))
	3.4b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	9.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	35.0b	(.f64 (exp.f64 (log.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	39.9b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2))) phi1)))))
	41.4b	(-.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))))))
	46.2b	(.f64 R (hypot.f64 (.f64 (+.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (*.f64 (-.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	33.2b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	9.6b	(.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))

Compiler

Compiled 35698 to 23591 computations (33.9% saved)

regimes1.6s (6.4%)

Accuracy

Total 0.1b remaining (3.5%)

Threshold costs 0.1b (3.5%)

Counts

113 → 1

Compiler

Compiled 37836 to 23942 computations (36.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-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	15	24
1	22	24
2	30	24
3	34	24
4	36	24
5	36	24

end256.0ms (1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 538 to 343 computations (36.2% saved)

Details

analyze2.9s (11.1%)

sample4.8s (18.7%)

simplify128.0ms (0.5%)

prune4.0ms (0%)

localize11.0ms (0%)

series2.0s (7.8%)

rewrite16.0ms (0.1%)

simplify328.0ms (1.3%)

prune812.0ms (3.1%)

localize13.0ms (0.1%)

series5.4s (20.8%)

rewrite13.0ms (0.1%)

simplify396.0ms (1.5%)

prune1.3s (5.1%)

localize25.0ms (0.1%)

series1.9s (7.4%)

rewrite16.0ms (0.1%)

simplify316.0ms (1.2%)

prune653.0ms (2.5%)

localize24.0ms (0.1%)

series1.9s (7.3%)

rewrite9.0ms (0%)

simplify299.0ms (1.2%)

prune672.0ms (2.6%)

regimes1.6s (6.4%)

simplify3.0ms (0%)

end256.0ms (1%)

Profiling