Details

analyze3.0s (15.1%)

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 (24.2%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.7s	6203×	body	128	valid
822.0ms	848×	body	1024	valid
589.0ms	766×	body	512	valid
560.0ms	2329×	body	128	invalid
491.0ms	507×	body	1024	invalid
221.0ms	358×	body	512	invalid
195.0ms	434×	body	256	valid
76.0ms	180×	body	256	invalid
10.0ms	5×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify118.0ms (0.6%)

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 (0.1%)

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)))
✓	3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (7.1%)

Counts

4 → 180

Calls

4 calls:

909.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
471.0ms	(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))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`associate-l_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 63

Calls

4 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)))
0.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))

simplify400.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1141×	`associate-r_binary64`
462×	`fma-def_binary64`
151×	`associate-l_binary64`
88×	`sub-neg_binary64`
65×	`associate-/l*_binary64`

Counts

243 → 263

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2275	46358
1	5160	46358

prune1.3s (6.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	250	13	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	13	264

Error

3.5b

Counts

264 → 13

Alt Table

Status	Error	Program
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	15.9b	(.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)))
	38.7b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	36.2b	(.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)))))
	4.9b	(.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)))))
	37.4b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.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 phi2))) (-.f64 phi1 phi2)))
	39.8b	(-.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))))))
	8.7b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.3b	(.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))))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
▶	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 60323 to 41254 computations (31.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.4b	(cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series44.0ms (0.2%)

Counts

3 → 72

Calls

3 calls:

20.0ms

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

18.0ms

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

5.0ms

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms

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

5.0ms

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

3.0ms

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

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
860×	`fma-neg_binary64`
664×	`cancel-sign-sub-inv_binary64`
258×	`associate-r_binary64`
234×	`distribute-rgt-neg-in_binary64`

Counts

146 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	3575
1	534	2723
2	1856	2456
3	4257	2412
4	4983	2412

prune555.0ms (2.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	215	15	230

Error

3.5b

Counts

230 → 15

Alt Table

Status	Error	Program
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.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) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	38.7b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	39.8b	(-.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))))))
	36.2b	(.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)))))
	4.9b	(.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)))))
	37.4b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	15.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) -1/2 (cos.f64 (*.f64 1/2 phi2)))) (-.f64 phi1 phi2)))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	8.7b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.3b	(.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))))
▶	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 9467 to 5516 computations (41.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.4b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series918.0ms (4.7%)

Counts

3 → 72

Calls

3 calls:

503.0ms

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

411.0ms

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

5.0ms

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

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

5.0ms

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

1.0ms

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

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

593×	`cancel-sign-sub-inv_binary64`
348×	`fma-neg_binary64`
345×	`neg-mul-1_binary64`
308×	`distribute-rgt-neg-in_binary64`
298×	`unswap-sqr_binary64`

Counts

165 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3909
1	655	3651
2	2239	3332
3	4444	3263
4	4993	3263

prune686.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	333	1	334
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	334	15	349

Error

3.5b

Counts

349 → 15

Alt Table

Status	Error	Program
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.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) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	38.7b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	9.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	39.8b	(-.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))))))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	8.7b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	36.2b	(.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)))))
	4.9b	(.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)))))
	37.4b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	15.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) -1/2 (cos.f64 (*.f64 1/2 phi2)))) (-.f64 phi1 phi2)))
	7.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
▶	4.3b	(.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))))

Compiler

Compiled 16061 to 9878 computations (38.5% saved)

localize15.0ms (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)))
✓	0.2b	(.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
✓	0.3b	(.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))))
	3.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.1s (10.6%)

Counts

2 → 88

Calls

2 calls:

1.2s

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

858.0ms

(*.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))))

rewrite14.0ms (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:

6.0ms

(*.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))))

simplify393.0ms (2%)

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 (6.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	315	14	329

Error

3.5b

Counts

329 → 14

Alt Table

Status	Error	Program
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	8.2b	(.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 1/2 phi1))) (-.f64 phi1 phi2))))
	9.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	38.7b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
✓	4.3b	(.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))))
	5.0b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (cbrt.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (cbrt.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))))
	36.2b	(.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)))))
	4.9b	(.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)))))
	9.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	15.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) -1/2 (cos.f64 (*.f64 1/2 phi2)))) (-.f64 phi1 phi2)))
	8.7b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	50.8b	(cbrt.f64 (.f64 (.f64 (.f64 R R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.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)))))))

Compiler

Compiled 66907 to 44834 computations (33% saved)

regimes2.0s (10.2%)

Accuracy

Total 0.2b remaining (5%)

Threshold costs 0.2b (5%)

Counts

180 → 1

Compiler

Compiled 55314 to 35885 computations (35.1% saved)

simplify2.0ms (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	17	24
1	26	24
2	33	24
3	37	24
4	39	24
5	38	24

end300.0ms (1.5%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 644 to 399 computations (38% saved)

Details

analyze3.0s (15.1%)

sample4.8s (24.2%)

simplify118.0ms (0.6%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series1.4s (7.1%)

rewrite17.0ms (0.1%)

simplify400.0ms (2%)

prune1.3s (6.8%)

localize16.0ms (0.1%)

series44.0ms (0.2%)

rewrite18.0ms (0.1%)

simplify101.0ms (0.5%)

prune555.0ms (2.8%)

localize15.0ms (0.1%)

series918.0ms (4.7%)

rewrite19.0ms (0.1%)

simplify120.0ms (0.6%)

prune686.0ms (3.5%)

localize15.0ms (0.1%)

series2.1s (10.6%)

rewrite14.0ms (0.1%)

simplify393.0ms (2%)

prune1.3s (6.8%)

regimes2.0s (10.2%)

simplify2.0ms (0%)

end300.0ms (1.5%)

Profiling