Details

analyze2.7s (15.2%)

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)

sample4.3s (23.9%)

Results

1.4s	6174×	body	128	valid
821.0ms	819×	body	1024	valid
542.0ms	2450×	body	128	invalid
509.0ms	825×	body	512	valid
468.0ms	490×	body	1024	invalid
212.0ms	380×	body	512	invalid
183.0ms	433×	body	256	valid
67.0ms	165×	body	256	invalid
8.0ms	5×	body	2048	valid

Compiler

Compiled 76 to 44 computations (42.1% saved)

preprocess66.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1000×	`distribute-rgt-in_binary64`
877×	`fma-def_binary64`
324×	`distribute-lft-in_binary64`
228×	`distribute-lft-neg-out_binary64`
228×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	264
1	261	264
2	662	264
3	2716	264
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify42.0ms (0.2%)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

4.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	39.0b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
▶	4.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

Status

Error

Program

39.0b

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

▶

4.2b

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

Compiler

Compiled 169 to 97 computations (42.6% 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)))
✓	2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.3s (7.5%)

Counts

4 → 180

Calls

45 calls:

328.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	phi2	0
313.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	phi1	0
190.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))	phi1	0
188.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))	phi2	0
36.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	R	-inf

rewrite75.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary64`
175×	`add-sqr-sqrt_binary64`
170×	`pow1_binary64`
169×	`*-un-lft-identity_binary64`
162×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	331	69
2	4502	69

Stop Event

1×	node limit

Counts

4 → 73

simplify313.0ms (1.7%)

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

prune1.2s (6.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	264	17	281
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	266	17	283

Error

3.8b

Counts

283 → 17

Alt Table

Status	Error	Program
	5.3b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	15.6b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)) (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1)) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	4.6b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	38.0b	(-.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))))))
	26.2b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2)) (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) (+.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))
	9.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	9.4b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	33.1b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	56.2b	(-.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))))))
	10.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	37.0b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	39.0b	(.f64 R (sqrt.f64 (+.f64 (.f64 phi2 phi2) (-.f64 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1) (.f64 phi1 phi1)) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (.f64 2 (+.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (*.f64 phi1 phi2)))))))
	24.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3) 1/3)) (-.f64 phi1 phi2)))
	25.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (-.f64 (.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)))
	17.0b	(.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)))
▶	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))

Compiler

Compiled 60298 to 41397 computations (31.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))
✓	0.4b	(log.f64 (exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
✓	2.4b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series42.0ms (0.2%)

Counts

4 → 120

Calls

30 calls:

6.0ms	(exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi1	0
3.0ms	(exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi2	0
3.0ms	(.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))	phi2	0
2.0ms	(.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))	phi1	0
2.0ms	(.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))	lambda1	-inf

rewrite54.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

935×	`prod-diff_binary64`
135×	`add-sqr-sqrt_binary64`
133×	`pow1_binary64`
132×	`*-un-lft-identity_binary64`
127×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	261	44
2	3436	44

Stop Event

1×	node limit

Counts

4 → 81

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

450×	`associate--l+_binary64`
415×	`associate--r+_binary64`
342×	`fma-neg_binary64`
273×	`associate-r_binary64`
229×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2642
1	591	2608
2	2218	2406

Stop Event

1×	node limit

Counts

201 → 117

prune249.0ms (1.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	118	16	134

Error

3.8b

Counts

134 → 16

Alt Table

Status	Error	Program
	26.2b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2)) (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) (+.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))
	9.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	17.0b	(.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)))
	15.2b	(.f64 R (hypot.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1) (-.f64 (.f64 (.f64 1/2 (.f64 phi2 (sin.f64 (.f64 1/2 phi1)))) (-.f64 lambda2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	9.4b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	33.1b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	56.2b	(-.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))))))
	10.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	37.0b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	39.0b	(.f64 R (sqrt.f64 (+.f64 (.f64 phi2 phi2) (-.f64 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1) (.f64 phi1 phi1)) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (.f64 2 (+.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (*.f64 phi1 phi2)))))))
	24.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3) 1/3)) (-.f64 phi1 phi2)))
	5.3b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	25.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (-.f64 (.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)))
▶	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))))) (-.f64 phi1 phi2)))
	4.6b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	5.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 3))) (-.f64 phi1 phi2)))

Compiler

Compiled 4532 to 2800 computations (38.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))
✓	0.4b	(log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))))
✓	0.5b	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3)
	2.4b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series30.0ms (0.2%)

Counts

3 → 72

Calls

18 calls:

4.0ms	(log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3))))	phi1	0
4.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3)	phi1	0
4.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3)	phi2	0
3.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3)	phi2	-inf
3.0ms	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3)	phi2	inf

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

576×	`prod-diff_binary64`
444×	`log-prod_binary64`
199×	`fma-def_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	241	30
2	2614	30

Stop Event

1×	node limit

Counts

3 → 95

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
496×	`cancel-sign-sub-inv_binary64`
471×	`unswap-sqr_binary64`
358×	`sub-neg_binary64`
344×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1418
1	326	1410
2	1227	1369
3	4230	1369

Stop Event

1×	node limit

Counts

167 → 93

prune245.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	137	9	146

Error

0.0b

Counts

146 → 9

Alt Table

Status	Error	Program
	24.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 3) 1/3)) (-.f64 phi1 phi2)))
	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 3))))) (-.f64 phi1 phi2)))
	5.3b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	4.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))) 3))))) (-.f64 phi1 phi2)))
▶	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))
	26.2b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2)) (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) (+.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))
	15.2b	(.f64 R (hypot.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) lambda1) (-.f64 (.f64 (.f64 1/2 (.f64 phi2 (sin.f64 (.f64 1/2 phi1)))) (-.f64 lambda2 lambda1)) (.f64 (cos.f64 (*.f64 1/2 phi1)) lambda2))) (-.f64 phi1 phi2)))
	33.1b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	39.0b	(.f64 R (sqrt.f64 (+.f64 (.f64 phi2 phi2) (-.f64 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1) (.f64 phi1 phi1)) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (.f64 2 (+.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (*.f64 phi1 phi2)))))))

Compiler

Compiled 4472 to 2789 computations (37.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.2s (12.4%)

Counts

4 → 156

Calls

39 calls:

328.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))	phi2	0
303.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))	phi1	0
169.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))	lambda1	-inf
169.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))	lambda2	inf
169.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.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))))) (-.f64 phi1 phi2)))	lambda2	-inf

rewrite35.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
245×	`pow1_binary64`
244×	`*-un-lft-identity_binary64`
230×	`add-exp-log_binary64`
230×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	109
1	467	69

Stop Event

1×	node limit

Counts

4 → 52

simplify440.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

533×	`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	2387	67673

Stop Event

1×	node limit

Counts

208 → 196

prune1.7s (9.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	197	8	205

Error

0.0b

Counts

205 → 8

Alt Table

Status	Error	Program
	5.3b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	0.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 1/2 phi2))))) 1) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))) (-.f64 phi1 phi2)))
	0.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 1/2 phi2)))) 3))) (-.f64 phi1 phi2)))
	26.2b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2)) (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) (+.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))
	0.1b	(.f64 R (hypot.f64 (-.f64 (fma.f64 lambda2 (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2))) (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1))) (fma.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1) (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 lambda2 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	33.1b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	39.0b	(.f64 R (sqrt.f64 (+.f64 (.f64 phi2 phi2) (-.f64 (+.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1) (.f64 phi1 phi1)) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (.f64 2 (+.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2))) (*.f64 phi1 phi2)))))))
	28.0b	(-.f64 (fma.f64 2 (.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 R (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1))))) (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 lambda2 R) (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)))))))))) (.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 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 R (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) lambda1))) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 R lambda1))))))

Compiler

Compiled 84887 to 64383 computations (24.2% saved)

regimes2.3s (12.7%)

Accuracy

Total 0.1b remaining (42.5%)

Threshold costs 0.1b (42.5%)

Counts

194 → 1

Compiler

Compiled 58734 to 43661 computations (25.7% saved)

simplify5.0ms (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	24	45
1	42	45
2	59	45
3	69	45
4	75	45
5	76	45

Stop Event

1×

saturated

end310.0ms (1.7%)

Stop Event

1×

fuel

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 682 to 512 computations (24.9% saved)

Details

analyze2.7s (15.2%)

sample4.3s (23.9%)

preprocess66.0ms (0.4%)

simplify42.0ms (0.2%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series1.3s (7.5%)

rewrite75.0ms (0.4%)

simplify313.0ms (1.7%)

prune1.2s (6.8%)

localize23.0ms (0.1%)

series42.0ms (0.2%)

rewrite54.0ms (0.3%)

simplify66.0ms (0.4%)

prune249.0ms (1.4%)

localize16.0ms (0.1%)

series30.0ms (0.2%)

rewrite49.0ms (0.3%)

simplify53.0ms (0.3%)

prune245.0ms (1.4%)

localize21.0ms (0.1%)

series2.2s (12.4%)

rewrite35.0ms (0.2%)

simplify440.0ms (2.5%)

prune1.7s (9.5%)

regimes2.3s (12.7%)

simplify5.0ms (0%)

end310.0ms (1.7%)

Profiling