Details

analyze3.6s (25%)

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)

sample127.0ms (0.9%)

Algorithm

1×

intervals

Results

26.0ms	192×	body	128	valid
16.0ms	23×	body	1024	valid
13.0ms	16×	body	1024	invalid
12.0ms	30×	body	512	valid
10.0ms	78×	body	128	invalid
5.0ms	12×	body	512	invalid
3.0ms	10×	body	256	valid
2.0ms	8×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify126.0ms (0.9%)

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

3.0b

Counts

3 → 1

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)))

Compiler

Compiled 95 to 55 computations (42.1% 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)))
✓	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite17.0ms (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:

6.0ms	(*.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)))
4.0ms	(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))

series2.8s (19.3%)

Counts

4 → 180

Calls

4 calls:

1.8s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
929.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
57.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify484.0ms (3.4%)

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 → 366

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2275	46358
1	5160	46358

prune1.2s (8.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	351	15	366
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	352	15	367

Error

2.8b

Counts

367 → 15

Alt Table

Status	Error	Program
	36.1b	(.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	54.4b	(-.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))))))
	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)))
	6.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.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))))
▶	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	38.6b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	26.1b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.1b	(.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)))
	9.1b	(.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 (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.1b	(.f64 (.f64 R (.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))))
	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))))

Compiler

Compiled 60345 to 41259 computations (31.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 13

Calls

1 calls:

4.0ms

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

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
571×	`associate-l_binary64`
446×	`associate-r_binary64`
437×	`distribute-rgt-neg-in_binary64`
386×	`fma-neg_binary64`

Counts

37 → 68

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	808
1	153	593
2	389	530
3	1042	504
4	3236	497
5	4880	497
6	5032	497

prune231.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	331	3	334
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	334	15	349

Error

2.8b

Counts

349 → 15

Alt Table

Status	Error	Program
	36.1b	(.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	54.4b	(-.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))))))
▶	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	38.6b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (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)))
	6.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.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))))
	6.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (*.f64 1/2 phi1))))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	26.1b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 phi2 (.f64 (sin.f64 (.f64 1/2 phi1)) -1/2) (cos.f64 (*.f64 1/2 phi1)))) (-.f64 phi1 phi2)))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	4.1b	(.f64 (.f64 R (.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))))
	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))))

Compiler

Compiled 5155 to 2962 computations (42.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune322.0ms (2.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	4559	1	4560
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	4560	15	4575

Error

2.8b

Counts

4575 → 15

Alt Table

Status	Error	Program
	36.1b	(.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	54.4b	(-.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))))))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	38.6b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (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)))
	6.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	6.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	26.1b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 phi2 (.f64 (sin.f64 (.f64 1/2 phi1)) -1/2) (cos.f64 (*.f64 1/2 phi1)))) (-.f64 phi1 phi2)))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (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))))
	4.1b	(.f64 (.f64 R (.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))))
	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))))

Compiler

Compiled 9100 to 5370 computations (41% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (-.f64 lambda1 lambda2))
	0.6b	(cbrt.f64 (-.f64 lambda1 lambda2))
✓	0.6b	(cbrt.f64 (-.f64 lambda1 lambda2))
	2.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
2×	`cbrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

2.0ms

(cbrt.f64 (-.f64 lambda1 lambda2))

series28.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

28.0ms

(cbrt.f64 (-.f64 lambda1 lambda2))

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
531×	`associate-r_binary64`
480×	`associate-l_binary64`
384×	`fma-def_binary64`
252×	`cancel-sign-sub-inv_binary64`

Counts

41 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1082
1	379	1060
2	1144	1019
3	4681	1019
4	5385	1019

prune265.0ms (1.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	5141	3	5144
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	5143	16	5159

Error

2.8b

Counts

5159 → 16

Alt Table

Status	Error	Program
	36.1b	(.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (sqrt.f64 (.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	54.4b	(-.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))))))
✓	3.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	38.6b	(cbrt.f64 (.f64 (.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))) (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	7.2b	(.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 1/2 phi1)))) (-.f64 phi1 phi2)))
	26.1b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	9.5b	(.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 1/2 phi2)))) (-.f64 phi1 phi2)))
	38.1b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))))
	14.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 phi2 (.f64 (sin.f64 (.f64 1/2 phi1)) -1/2) (cos.f64 (*.f64 1/2 phi1)))) (-.f64 phi1 phi2)))
	6.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (-.f64 phi1 phi2)))
	9.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	22.0b	(.f64 R (hypot.f64 (.f64 (.f64 (.f64 (pow.f64 (.f64 -1 lambda1) 1/3) (cbrt.f64 -1)) (cbrt.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (-.f64 lambda1 lambda2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (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))))
	4.1b	(.f64 (.f64 R (.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))))
	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))))

Compiler

Compiled 8095 to 3936 computations (51.4% saved)

regimes1.3s (9.2%)

Accuracy

Total 0.2b remaining (4.8%)

Threshold costs 0.2b (4.8%)

Compiler

Compiled 30483 to 20072 computations (34.2% saved)

simplify4.0ms (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

end21.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 105 to 70 computations (33.3% saved)

sample3.5s (24.6%)

Algorithm

1×

intervals

Results

811.0ms	6046×	body	128	valid
566.0ms	793×	body	1024	valid
339.0ms	753×	body	512	valid
328.0ms	454×	body	1024	invalid
320.0ms	2442×	body	128	invalid
151.0ms	354×	body	512	invalid
115.0ms	399×	body	256	valid
51.0ms	176×	body	256	invalid
17.0ms	9×	body	2048	valid

Compiler

Compiled 677 to 414 computations (38.8% saved)

Details

analyze3.6s (25%)

sample127.0ms (0.9%)

simplify126.0ms (0.9%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite17.0ms (0.1%)

series2.8s (19.3%)

simplify484.0ms (3.4%)

prune1.2s (8.4%)

localize15.0ms (0.1%)

rewrite5.0ms (0%)

series5.0ms (0%)

simplify85.0ms (0.6%)

prune231.0ms (1.6%)

localize22.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify43.0ms (0.3%)

prune322.0ms (2.2%)

localize15.0ms (0.1%)

rewrite3.0ms (0%)

series28.0ms (0.2%)

simplify111.0ms (0.8%)

prune265.0ms (1.8%)

regimes1.3s (9.2%)

simplify4.0ms (0%)

end21.0ms (0.1%)

sample3.5s (24.6%)

Profiling