Details

analyze2.7s (12.3%)

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)

sample4.2s (18.7%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.4s	6204×	body	128	valid
746.0ms	815×	body	1024	valid
582.0ms	2491×	body	128	invalid
450.0ms	753×	body	512	valid
412.0ms	463×	body	1024	invalid
217.0ms	370×	body	512	invalid
193.0ms	481×	body	256	valid
61.0ms	159×	body	256	invalid
5.0ms	3×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify131.0ms (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

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

3.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
	38.2b	(.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)))))

Status

Error

Program

▶

3.0b

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

38.2b

(*.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)))))

Compiler

Compiled 169 to 97 computations (42.6% saved)

localize12.0ms (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)))
✓	2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.1s (18.4%)

Counts

4 → 180

Calls

4 calls:

3.1s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.0s	(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)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite295.0ms (1.3%)

Algorithm

4×	egg-rewrite

Rules

35×	`egg`
29×	`egg`
19×	`egg`
18×	`egg`

Counts

4 → 101

Calls

4 calls:

86.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
77.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
68.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
63.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	157	9
2	1975	9
3	5759	9
0	11	15
1	246	15
2	3189	15
3	4929	15
0	15	24
1	331	24
2	4247	24
3	5102	24
0	13	21
1	292	21
2	3788	21
3	5204	21

simplify645.0ms (2.9%)

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

281 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2196	44761
1	5035	44761

prune1.7s (7.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	280	17	297
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	281	18	299

Error

2.7b

Counts

299 → 18

Alt Table

Status	Error	Program
	25.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.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)))
	28.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	33.6b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) 2)
	3.5b	(.f64 R (hypot.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (pow.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
▶	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	57.8b	(-.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))))))
	50.1b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) 3) 1/3)
	3.2b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	38.2b	(.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)))))
	3.4b	(.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) R))
	8.0b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))) (-.f64 phi1 phi2)))
	7.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	44.2b	(-.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)))))))
	17.9b	(.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)))
	4.3b	(.f64 (.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)) (pow.f64 (cbrt.f64 R) 2)) (cbrt.f64 R))
	4.2b	(.f64 (.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) 2)) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))

Compiler

Compiled 60964 to 41678 computations (31.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.5b	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
	2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series692.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

662.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
16.0ms	(+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
14.0ms	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

rewrite288.0ms (1.3%)

Algorithm

3×	egg-rewrite

Rules

48×	`egg`
26×	`egg`
20×	`egg`

Counts

3 → 94

Calls

3 calls:

117.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
115.0ms	(+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
54.0ms	(expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	214	9
2	2621	9
3	4699	9
4	4756	9
5	5004	9
0	8	11
1	174	11
2	2156	11
3	6179	11
0	10	14
1	216	11
2	2612	11
3	4705	11
4	4767	11
5	4961	11

simplify122.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

771×	`cancel-sign-sub-inv_binary64`
384×	`associate--l+_binary64`
381×	`associate--r+_binary64`
336×	`distribute-rgt-neg-in_binary64`
325×	`distribute-lft-neg-in_binary64`

Counts

166 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1930
1	401	1911
2	1487	1701
3	4217	1701
4	4902	1701
5	4982	1701

prune400.0ms (1.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	171	19	190

Error

2.7b

Counts

190 → 19

Alt Table

Status	Error	Program
	25.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.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)))
	28.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	33.6b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) 2)
	3.5b	(.f64 R (hypot.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (pow.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	57.8b	(-.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))))))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 2)))) (-.f64 phi1 phi2)))
	7.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
▶	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	38.2b	(.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)))))
	3.4b	(.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) R))
	8.0b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	44.2b	(-.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)))))))
	17.9b	(.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)))
	4.3b	(.f64 (.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)) (pow.f64 (cbrt.f64 R) 2)) (cbrt.f64 R))
	4.2b	(.f64 (.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) 2)) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (sqrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 6721 to 4224 computations (37.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
✓	0.5b	(log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.1s (9.3%)

Counts

3 → 96

Calls

3 calls:

1.0s

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

755.0ms

(log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

278.0ms

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

rewrite175.0ms (0.8%)

Algorithm

3×	egg-rewrite

Rules

40×	`egg`
37×	`egg`
29×	`egg`

Counts

3 → 106

Calls

3 calls:

67.0ms

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

54.0ms

(log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))

52.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	9
1	218	9
2	2384	9
3	5039	9
0	14	21
1	307	15
2	3600	15
3	5321	15
0	9	13
1	201	11
2	2373	11
3	5032	11

simplify146.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

202 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2272
1	575	2242
2	2109	2049
3	4884	2049
4	4986	2049
5	4985	2049

prune350.0ms (1.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	15	17
Picked	0	1	1
Done	0	1	1
Total	188	19	207

Error

2.7b

Counts

207 → 19

Alt Table

Status	Error	Program
	33.6b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) 2)
	3.5b	(.f64 R (hypot.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (pow.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	57.8b	(-.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))))))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 2)))) (-.f64 phi1 phi2)))
	7.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
▶	3.2b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	4.3b	(.f64 (.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)) (pow.f64 (cbrt.f64 R) 2)) (cbrt.f64 R))
	17.3b	(.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)))
	38.2b	(.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)))))
	3.4b	(.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) R))
	8.0b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	25.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.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)))
	44.2b	(-.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)))))))
	4.2b	(.f64 (.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) 2)) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (sqrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))))) (-.f64 phi1 phi2)))
	16.5b	(.f64 R (hypot.f64 (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda2)) (-.f64 phi1 phi2)))

Compiler

Compiled 6605 to 3866 computations (41.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2)))
✓	0.4b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
✓	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.0s (4.5%)

Counts

3 → 96

Calls

3 calls:

497.0ms

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

485.0ms

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

25.0ms

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

rewrite177.0ms (0.8%)

Algorithm

3×	egg-rewrite

Rules

43×	`egg`
23×	`egg`
21×	`egg`

Counts

3 → 87

Calls

3 calls:

68.0ms

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

58.0ms

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

50.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	174	11
2	2159	11
3	6160	11
0	9	14
1	196	12
2	2301	12
3	4869	12
0	14	15
1	306	15
2	3799	15
3	5513	15

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

885×	`cancel-sign-sub-inv_binary64`
320×	`associate-r_binary64`
273×	`unswap-sqr_binary64`
230×	`associate-l_binary64`
228×	`sub-neg_binary64`

Counts

183 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	2640
1	740	2628
2	2719	2612
3	5140	2612

prune633.0ms (2.8%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	240	5	245
Fresh	1	15	16
Picked	1	0	1
Done	0	2	2
Total	242	22	264

Error

2.7b

Counts

264 → 22

Alt Table

Status	Error	Program
	33.6b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) 2)
	3.5b	(.f64 R (hypot.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (pow.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) 2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (-.f64 phi1 phi2)))
	57.8b	(-.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))))))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 2)))) (-.f64 phi1 phi2)))
	7.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	4.3b	(.f64 (.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)) (pow.f64 (cbrt.f64 R) 2)) (cbrt.f64 R))
	17.3b	(.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)))
	3.3b	(.f64 R (hypot.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 3) 2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	38.2b	(.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)))))
	3.4b	(.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) R))
	7.6b	(.f64 R (hypot.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2)) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	16.5b	(.f64 R (hypot.f64 (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda2)) (-.f64 phi1 phi2)))
	7.6b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 phi1))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 phi1))) 2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	8.0b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	25.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.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)))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (pow.f64 (E.f64) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	44.2b	(-.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)))))))
	7.2b	(.f64 R (hypot.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 phi2))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	6.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (+.f64 1 (sqrt.f64 (pow.f64 (expm1.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 10284 to 6457 computations (37.2% saved)

regimes1.9s (8.4%)

Accuracy

Total 0.3b remaining (8.9%)

Threshold costs 0.3b (8.9%)

Counts

158 → 1

Compiler

Compiled 49461 to 34325 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	28	35
2	41	35
3	49	35
4	54	35
5	55	35
6	55	35

end433.0ms (1.9%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 846 to 568 computations (32.9% saved)

Details

analyze2.7s (12.3%)

sample4.2s (18.7%)

simplify131.0ms (0.6%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series4.1s (18.4%)

rewrite295.0ms (1.3%)

simplify645.0ms (2.9%)

prune1.7s (7.4%)

localize25.0ms (0.1%)

series692.0ms (3.1%)

rewrite288.0ms (1.3%)

simplify122.0ms (0.5%)

prune400.0ms (1.8%)

localize17.0ms (0.1%)

series2.1s (9.3%)

rewrite175.0ms (0.8%)

simplify146.0ms (0.7%)

prune350.0ms (1.6%)

localize17.0ms (0.1%)

series1.0s (4.5%)

rewrite177.0ms (0.8%)

simplify81.0ms (0.4%)

prune633.0ms (2.8%)

regimes1.9s (8.4%)

simplify3.0ms (0%)

end433.0ms (1.9%)

Profiling