Details

analyze2.8s (14.6%)

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 (24.9%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.5s	6299×	body	128	valid
862.0ms	797×	body	1024	valid
628.0ms	2516×	body	128	invalid
515.0ms	376×	body	512	invalid
458.0ms	492×	body	1024	invalid
449.0ms	729×	body	512	valid
209.0ms	425×	body	256	valid
74.0ms	191×	body	256	invalid
10.0ms	6×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify113.0ms (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

2.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.1b	(.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)

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)))
✓	1.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.9s (15%)

Counts

4 → 180

Calls

4 calls:

1.9s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
971.0ms	(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))

rewrite15.0ms (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	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
3.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
0.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))

simplify405.0ms (2.1%)

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

prune1.2s (6.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	251	12	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	252	12	264

Error

1.8b

Counts

264 → 12

Alt Table

Status	Error	Program
	7.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	16.5b	(.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)))
	2.5b	(.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 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	36.3b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	46.8b	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2) lambda1))))) R)
	26.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.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)))
	24.1b	(.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)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (.f64 (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	3.3b	(.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)))))
▶	2.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.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 60319 to 41272 computations (31.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (*.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))))
✓	0.4b	(*.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)))
	1.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.1s (5.8%)

Counts

3 → 96

Calls

3 calls:

610.0ms

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

483.0ms

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

24.0ms

(*.f64 (*.f64 (-.f64 lambda1 lambda2) (*.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))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 83

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (-.f64 lambda1 lambda2) (*.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)))

simplify108.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

890×	`cancel-sign-sub-inv_binary64`
483×	`associate-r_binary64`
405×	`associate-l_binary64`
306×	`unswap-sqr_binary64`
235×	`*-commutative_binary64`

Counts

179 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	4768
1	927	4506
2	3414	4252
3	5804	4252

prune742.0ms (3.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	332	4	336
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	334	14	348

Error

1.8b

Counts

348 → 14

Alt Table

Status	Error	Program
	7.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	16.5b	(.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)))
	2.5b	(.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 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	36.3b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	46.8b	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2) lambda1))))) R)
	26.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.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)))
	24.1b	(.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)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (.f64 (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
▶	2.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (exp.f64 (log.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)))
	7.6b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	20.2b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 1/3))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	2.4b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))

Compiler

Compiled 16666 to 10254 computations (38.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.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)))
	1.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
✓	3.8b	(log.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

series1.3s (6.8%)

Counts

1 → 24

Calls

1 calls:

1.3s	(log.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
9×	`log-pow_binary64`
6×	`pow1/3_binary64`
4×	`add-exp-log_binary64`
2×	`rem-log-exp_binary64`

Counts

1 → 21

Calls

1 calls:

3.0ms

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

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

748×	`times-frac_binary64`
459×	`associate-/l*_binary64`
322×	`associate-r_binary64`
283×	`associate-/r*_binary64`
274×	`associate-l_binary64`

Counts

45 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1246
1	285	1065
2	963	1009
3	5210	1009

prune752.0ms (3.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	321	1	322
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	322	14	336

Error

1.8b

Counts

336 → 14

Alt Table

Status	Error	Program
	7.6b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (exp.f64 (log.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) 1/3)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (.f64 (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	16.5b	(.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)))
	2.5b	(.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 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	36.3b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	46.8b	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2) lambda1))))) R)
	26.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.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)))
	24.1b	(.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)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
✓	2.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (exp.f64 (log.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)))
	20.2b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 1/3))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
▶	2.4b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))

Compiler

Compiled 16789 to 10706 computations (36.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.8b	(pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)
	1.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
✓	1.7b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

series531.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

526.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
9×	`unpow-prod-down_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

3.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

991×	`fma-neg_binary64`
454×	`fma-def_binary64`
400×	`*-commutative_binary64`
379×	`cancel-sign-sub-inv_binary64`
272×	`sub-neg_binary64`

Counts

83 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1837
1	430	1735
2	1326	1676
3	3526	1670
4	4858	1670
5	5007	1670

prune361.0ms (1.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	152	14	166

Error

1.8b

Counts

166 → 14

Alt Table

Status	Error	Program
	7.6b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (exp.f64 (log.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) 1/3)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (.f64 (.f64 (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (cbrt.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.5b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	16.5b	(.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)))
	20.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)))) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 1/3)) (-.f64 phi1 phi2)))
	2.5b	(.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 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	36.3b	(.f64 (sqrt.f64 R) (.f64 (sqrt.f64 R) (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))))
	46.8b	(.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 lambda1 lambda1) (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2) lambda1))))) R)
	26.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) (.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)))
	24.1b	(.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)))
	7.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
✓	2.3b	(.f64 R (hypot.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (exp.f64 (log.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)))
✓	2.4b	(.f64 R (hypot.f64 (.f64 (*.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))

Compiler

Compiled 7209 to 4759 computations (34% saved)

regimes1.6s (8.4%)

Accuracy

Total 0.3b remaining (7.2%)

Threshold costs 0.3b (7.2%)

Counts

145 → 1

Compiler

Compiled 44190 to 30926 computations (30% 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	15	24
1	22	24
2	30	24
3	34	24
4	36	24
5	36	24

end297.0ms (1.5%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 598 to 406 computations (32.1% saved)

Details

analyze2.8s (14.6%)

sample4.8s (24.9%)

simplify113.0ms (0.6%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series2.9s (15%)

rewrite15.0ms (0.1%)

simplify405.0ms (2.1%)

prune1.2s (6.1%)

localize17.0ms (0.1%)

series1.1s (5.8%)

rewrite21.0ms (0.1%)

simplify108.0ms (0.6%)

prune742.0ms (3.8%)

localize19.0ms (0.1%)

series1.3s (6.8%)

rewrite4.0ms (0%)

simplify39.0ms (0.2%)

prune752.0ms (3.9%)

localize25.0ms (0.1%)

series531.0ms (2.7%)

rewrite7.0ms (0%)

simplify91.0ms (0.5%)

prune361.0ms (1.9%)

regimes1.6s (8.4%)

simplify2.0ms (0%)

end297.0ms (1.5%)

Profiling