Details

analyze2.8s (10.1%)

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)

sample4.2s (15.2%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.4s	6209×	body	128	valid
777.0ms	843×	body	1024	valid
541.0ms	2458×	body	128	invalid
494.0ms	760×	body	512	valid
408.0ms	443×	body	1024	invalid
195.0ms	343×	body	512	invalid
179.0ms	434×	body	256	valid
57.0ms	141×	body	256	invalid
16.0ms	10×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify114.0ms (0.4%)

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
	37.0b	(.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)))))
▶	3.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

Status

Error

Program

37.0b

(*.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)))))

▶

3.0b

(*.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%)

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)))
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.7s (6.3%)

Counts

4 → 180

Calls

4 calls:

1.2s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
458.0ms	(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)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite16.0ms (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:

5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.0ms	(.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))

simplify397.0ms (1.5%)

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 (4.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	248	15	263
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	250	15	265

Error

2.7b

Counts

265 → 15

Alt Table

Status	Error	Program
	56.0b	(-.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))))))
	15.3b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	33.5b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	8.2b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	6.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	3.4b	(.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))))
	33.5b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (+.f64 (.f64 lambda1 lambda1) (+.f64 (.f64 lambda2 lambda2) (*.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	4.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
▶	3.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	30.0b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	23.3b	(.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)))
	3.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	44.1b	(-.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)))))))

Compiler

Compiled 60329 to 41276 computations (31.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series840.0ms (3.1%)

Counts

3 → 132

Calls

3 calls:

811.0ms

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

22.0ms

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

7.0ms

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

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`log-prod_binary64`

Counts

3 → 71

Calls

3 calls:

9.0ms

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

5.0ms

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

3.0ms

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

simplify311.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

203 → 248

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1422	25780
1	4749	25607
2	5140	25607

prune819.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	269	2	271
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	272	14	286

Error

2.7b

Counts

286 → 14

Alt Table

Status	Error	Program
	56.0b	(-.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))))))
	15.3b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	33.5b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	33.5b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (+.f64 (.f64 lambda1 lambda1) (+.f64 (.f64 lambda2 lambda2) (*.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	4.2b	(.f64 (.f64 (cbrt.f64 R) (cbrt.f64 R)) (.f64 (cbrt.f64 R) (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	30.0b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	8.2b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	23.3b	(.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)))
▶	3.4b	(.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))))
	3.4b	(.f64 R (hypot.f64 (.f64 (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	44.1b	(-.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)))))))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (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)))

Compiler

Compiled 35014 to 23217 computations (33.7% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.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))))
✓	0.3b	(.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))))
	2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.0s (7.3%)

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))))

806.0ms

(*.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))))

rewrite13.0ms (0%)

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))))

3.0ms

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

simplify381.0ms (1.4%)

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 (4.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	309	5	314
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	316	12	328

Error

2.7b

Counts

328 → 12

Alt Table

Status	Error	Program
	56.0b	(-.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))))))
	15.3b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	33.5b	(exp.f64 (+.f64 (log.f64 R) (log.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	3.5b	(.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 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2))))
	32.7b	(.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))))
	8.2b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
▶	3.5b	(.f64 (.f64 (.f64 R (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (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	(.f64 (.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (fabs.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	8.0b	(.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))))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (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)))

Compiler

Compiled 67189 to 45013 computations (33% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 R (sqrt.f64 (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 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
✓	0.3b	(.f64 (.f64 (.f64 R (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (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))))
	2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series6.5s (23.6%)

Counts

3 → 148

Calls

3 calls:

4.5s

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

1.2s

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

806.0ms

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

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-prod_binary64`
24×	`associate-r_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`

Counts

3 → 80

Calls

3 calls:

9.0ms

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

9.0ms

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

5.0ms

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

simplify650.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
267×	`associate-l_binary64`
105×	`sqr-pow_binary64`
93×	`sub-neg_binary64`
72×	`associate-/l*_binary64`

Counts

228 → 314

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2998	74814
1	5248	74814

prune2.0s (7.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	379	4	383
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	381	14	395

Error

2.6b

Counts

395 → 14

Alt Table

Status	Error	Program
✓	3.5b	(.f64 (.f64 (.f64 R (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (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))))
	43.8b	(.f64 (.f64 (.f64 R (pow.f64 phi2 1/4)) (sqrt.f64 (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))))
	7.3b	(.f64 (.f64 (.f64 R (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (.f64 1/2 phi2))) (-.f64 phi1 phi2))))) (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	56.0b	(-.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))))))
	15.3b	(.f64 R (hypot.f64 (neg.f64 (.f64 lambda2 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 phi1 phi2)))
	3.5b	(.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 (cbrt.f64 (-.f64 lambda1 lambda2)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2))))
	8.2b	(.f64 R (exp.f64 (log.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	3.7b	(.f64 (.f64 (.f64 R (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (fabs.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))) (sqrt.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	32.8b	(.f64 (.f64 (exp.f64 (log.f64 (.f64 R (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))) (sqrt.f64 (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))))
	33.7b	(exp.f64 (+.f64 (+.f64 (+.f64 (log.f64 R) (log.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (log.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))) (log.f64 (sqrt.f64 (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi2))))) (-.f64 phi1 phi2)))
	14.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	8.0b	(.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))))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))

Compiler

Compiled 106622 to 71609 computations (32.8% saved)

regimes1.8s (6.6%)

Accuracy

Total 0.2b remaining (6%)

Threshold costs 0.2b (6%)

Counts

164 → 1

Compiler

Compiled 51831 to 32384 computations (37.5% 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

end301.0ms (1.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 678 to 416 computations (38.6% saved)

Details

analyze2.8s (10.1%)

sample4.2s (15.2%)

simplify114.0ms (0.4%)

prune5.0ms (0%)

localize13.0ms (0%)

series1.7s (6.3%)

rewrite16.0ms (0.1%)

simplify397.0ms (1.5%)

prune1.3s (4.7%)

localize17.0ms (0.1%)

series840.0ms (3.1%)

rewrite22.0ms (0.1%)

simplify311.0ms (1.1%)

prune819.0ms (3%)

localize13.0ms (0%)

series2.0s (7.3%)

rewrite13.0ms (0%)

simplify381.0ms (1.4%)

prune1.3s (4.6%)

localize16.0ms (0.1%)

series6.5s (23.6%)

rewrite33.0ms (0.1%)

simplify650.0ms (2.4%)

prune2.0s (7.2%)

regimes1.8s (6.6%)

simplify2.0ms (0%)

end301.0ms (1.1%)

Profiling