Details

analyze2.7s (19.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample4.0s (28.7%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.3s	6252×	body	128	valid
702.0ms	788×	body	1024	valid
533.0ms	2537×	body	128	invalid
465.0ms	506×	body	1024	invalid
445.0ms	769×	body	512	valid
194.0ms	359×	body	512	invalid
183.0ms	442×	body	256	valid
61.0ms	156×	body	256	invalid
8.0ms	5×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify23.0ms (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

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

3.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.4b	(.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 (0.1%)

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)))
✓	3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (10.3%)

Counts

4 → 180

Calls

4 calls:

886.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
508.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
22.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 73

Calls

4 calls:

60.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
60.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
60.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
60.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify279.0ms (2%)

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 (8.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	267	14	281
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	14	282

Error

3.0b

Counts

282 → 14

Alt Table

Status	Error	Program
	40.8b	(-.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))))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	26.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 (.f64 1/48 (.f64 (pow.f64 phi1 3) (sin.f64 (.f64 1/2 phi2)))) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	3.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	55.5b	(-.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))))))
	34.5b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	31.3b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	29.3b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	8.5b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	17.1b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))) (-.f64 phi1 phi2)))
	61.2b	(log.f64 (+.f64 1 (expm1.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	51.0b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	7.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
▶	3.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 60020 to 41213 computations (31.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
✓	0.4b	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
✓	3.0b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series429.0ms (3.1%)

Counts

4 → 120

Calls

4 calls:

397.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
23.0ms	(.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))
5.0ms	(expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
4.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

970×	`prod-diff_binary64`
131×	`add-sqr-sqrt_binary64`
128×	`expm1-log1p-u_binary64`
127×	`log1p-expm1-u_binary64`
124×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	259	44
2	3417	44

Stop Event

1×	node limit

Counts

4 → 79

Calls

4 calls:

53.0ms	(.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))
53.0ms	(expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
53.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
53.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
620×	`cancel-sign-sub-inv_binary64`
249×	`fma-neg_binary64`
217×	`sub-neg_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2689
1	610	2669
2	2324	2609

Stop Event

1×	node limit

Counts

199 → 116

prune226.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	117	13	130

Error

2.9b

Counts

130 → 13

Alt Table

Status	Error	Program
	8.5b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
▶	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	40.8b	(-.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))))))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))
	26.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 (.f64 1/48 (.f64 (pow.f64 phi1 3) (sin.f64 (.f64 1/2 phi2)))) (fma.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2))) (.f64 1/8 (.f64 (.f64 phi1 phi1) (cos.f64 (.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	3.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	31.3b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	29.3b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	17.1b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))) (-.f64 phi1 phi2)))
	12.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 phi1 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) (sin.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (/.f64 (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) 2) (.f64 phi1 phi1))) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 (cos.f64 (*.f64 1/2 phi2)) 1)))))))) (-.f64 phi1 phi2)))
	55.5b	(-.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))))))
	51.0b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	7.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))

Compiler

Compiled 4556 to 2863 computations (37.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)))))
✓	0.3b	(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))
✓	0.4b	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)
	3.0b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series39.0ms (0.3%)

Counts

3 → 96

Calls

3 calls:

22.0ms

(*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))))

12.0ms

(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)

4.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

373×	`fma-def_binary64`
265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
192×	`fma-neg_binary64`
148×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	322	36
2	3831	36

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

55.0ms

(*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))))

55.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))

55.0ms

(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

731×	`cancel-sign-sub-inv_binary64`
330×	`associate--l+_binary64`
321×	`associate--r+_binary64`
317×	`fma-neg_binary64`
281×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2066
1	498	2057
2	1809	1917

Stop Event

1×	node limit

Counts

169 → 128

prune307.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	164	14	178

Error

2.9b

Counts

178 → 14

Alt Table

Status	Error	Program
	8.5b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
✓	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	40.8b	(-.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))))))
	26.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) (-.f64 (.f64 (pow.f64 phi1 3) 1/48) (.f64 1/2 phi1)))) (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (*.f64 phi1 phi1) -1/8)))) (-.f64 phi1 phi2)))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))
	17.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 (sin.f64 (*.f64 1/2 phi2))))))))) (-.f64 phi1 phi2)))
▶	3.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	31.3b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	29.3b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	17.1b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))) (-.f64 phi1 phi2)))
	12.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 phi1 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) (sin.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (/.f64 (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) 2) (.f64 phi1 phi1))) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 (cos.f64 (*.f64 1/2 phi2)) 1)))))))) (-.f64 phi1 phi2)))
	55.5b	(-.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))))))
	51.0b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	7.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))

Compiler

Compiled 5682 to 3452 computations (39.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2))) 3))
✓	0.5b	(cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
✓	0.5b	(pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)
	3.0b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series747.0ms (5.4%)

Counts

3 → 96

Calls

3 calls:

376.0ms

(pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)

347.0ms

(cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))

24.0ms

(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3))

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

935×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	299	35
2	3696	35

Stop Event

1×	node limit

Counts

3 → 65

Calls

3 calls:

57.0ms

(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3))

57.0ms

(cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))

57.0ms

(pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

777×	`cancel-sign-sub-inv_binary64`
260×	`distribute-rgt-neg-in_binary64`
255×	`fma-neg_binary64`
249×	`associate-r_binary64`
239×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	2252
1	631	2236
2	2328	2094

Stop Event

1×	node limit

Counts

161 → 122

prune266.0ms (1.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	159	14	173

Error

2.9b

Counts

173 → 14

Alt Table

Status	Error	Program
	8.5b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
✓	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	40.8b	(-.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))))))
	26.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) (-.f64 (.f64 (pow.f64 phi1 3) 1/48) (.f64 1/2 phi1)))) (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 (*.f64 phi1 phi1) -1/8)))) (-.f64 phi1 phi2)))
	8.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 phi2))) 3)) (-.f64 phi1 phi2)))
	17.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (-.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 (sin.f64 (*.f64 1/2 phi2))))))))) (-.f64 phi1 phi2)))
✓	3.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	31.3b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	29.3b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	17.1b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))) (-.f64 phi1 phi2)))
	12.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (fma.f64 1/2 (/.f64 phi1 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) (sin.f64 (.f64 1/2 phi2)))) (.f64 1/8 (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (/.f64 (pow.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) 2) (.f64 phi1 phi1))) (/.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 phi1 phi1)) (+.f64 (cos.f64 (*.f64 1/2 phi2)) 1)))))))) (-.f64 phi1 phi2)))
	55.5b	(-.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))))))
	51.0b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)

Compiler

Compiled 5295 to 3253 computations (38.6% saved)

regimes1.4s (10.4%)

Accuracy

Total 0.3b remaining (7.7%)

Threshold costs 0.3b (7.7%)

Counts

139 → 1

Compiler

Compiled 32598 to 23483 computations (28% saved)

simplify2.0ms (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	16	26
1	24	26
2	32	26
3	36	26
4	38	26

Stop Event

1×

saturated

end269.0ms (1.9%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 535 to 379 computations (29.2% saved)

Details

analyze2.7s (19.7%)

sample4.0s (28.7%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series1.4s (10.3%)

rewrite61.0ms (0.4%)

simplify279.0ms (2%)

prune1.2s (8.9%)

localize15.0ms (0.1%)

series429.0ms (3.1%)

rewrite56.0ms (0.4%)

simplify56.0ms (0.4%)

prune226.0ms (1.6%)

localize17.0ms (0.1%)

series39.0ms (0.3%)

rewrite57.0ms (0.4%)

simplify49.0ms (0.4%)

prune307.0ms (2.2%)

localize15.0ms (0.1%)

series747.0ms (5.4%)

rewrite58.0ms (0.4%)

simplify52.0ms (0.4%)

prune266.0ms (1.9%)

regimes1.4s (10.4%)

simplify2.0ms (0%)

end269.0ms (1.9%)

Profiling