Details

analyze2.7s (17.2%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 25 to 15 computations (40% saved)

sample310.0ms (2%)

Algorithm

1×

intervals

Results

145.0ms	149×	body	1024	valid
34.0ms	58×	body	512	valid
5.0ms	17×	body	256	valid
5.0ms	31×	body	128	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
141×	`fma-neg_binary64`
44×	`distribute-rgt-in_binary64`
38×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

prune4.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Status

Error

Program

▶

0.4b

(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

0.4b

(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 137 to 71 computations (48.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
✓	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	3.7b	(sin.f64 (-.f64 lambda1 lambda2))
✓	3.8b	(cos.f64 (-.f64 lambda1 lambda2))

series48.0ms (0.3%)

Counts

4 → 64

Calls

4 calls:

31.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
9.0ms	(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`sin-sum_binary64`

Counts

4 → 65

Calls

4 calls:

4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
0.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
0.0ms	(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

633×	`cancel-sign-sub-inv_binary64`
596×	`fma-def_binary64`
520×	`sub-neg_binary64`
381×	`*-commutative_binary64`
340×	`unsub-neg_binary64`

Counts

129 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	3217
1	522	2562
2	1534	2368
3	3855	2292
4	4587	2292
5	4928	2292

prune207.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	139	10	149
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	141	10	151

Error

0.2b

Counts

151 → 10

Alt Table

Status	Error	Program
	4.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 lambda1 (+.f64 (cos.f64 lambda2) (.f64 (.f64 1/2 (sin.f64 lambda2)) lambda1))) (sin.f64 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	36.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	32.3b	(+.f64 lambda1 (.f64 (sqrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (sqrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))

Compiler

Compiled 5671 to 1527 computations (73.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))
✓	0.6b	(fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))
	3.7b	(sin.f64 (-.f64 lambda1 lambda2))
	3.8b	(cos.f64 (-.f64 lambda1 lambda2))

series590.0ms (3.8%)

Counts

2 → 72

Calls

2 calls:

559.0ms	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))
31.0ms	(fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 21

Calls

2 calls:

0.0ms	(fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))
0.0ms	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

909×	`times-frac_binary64`
531×	`fma-def_binary64`
440×	`cancel-sign-sub-inv_binary64`
137×	`sub-neg_binary64`
125×	`associate-r_binary64`

Counts

93 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1927
1	515	1850
2	1842	1754
3	5020	1754

prune310.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Error

0.2b

Counts

172 → 9

Alt Table

Status	Error	Program
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	4.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	26.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (cos.f64 phi1))))
	32.3b	(+.f64 lambda1 (.f64 (sqrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (sqrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
▶	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 lambda1 (+.f64 (cos.f64 lambda2) (.f64 (.f64 1/2 (sin.f64 lambda2)) lambda1))) (sin.f64 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))

Compiler

Compiled 6546 to 1986 computations (69.7% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	0.8b	(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	3.7b	(sin.f64 (-.f64 lambda1 lambda2))
	3.8b	(cos.f64 (-.f64 lambda1 lambda2))

series30.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

30.0ms

(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary64`
4×	`log-pow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
493×	`distribute-rgt-neg-in_binary64`
361×	`associate-r_binary64`
360×	`cancel-sign-sub-inv_binary64`
332×	`fma-def_binary64`

Counts

66 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1364
1	299	1293
2	892	1239
3	3120	1227
4	5053	1227

prune416.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	197	10	207

Error

0.2b

Counts

207 → 10

Alt Table

Status	Error	Program
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	4.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	26.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (cos.f64 phi1))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	14.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))))))
✓	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 lambda1 (+.f64 (cos.f64 lambda2) (.f64 (.f64 1/2 (sin.f64 lambda2)) lambda1))) (sin.f64 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	14.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))

Compiler

Compiled 7351 to 2068 computations (71.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	1.2b	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))
	3.7b	(sin.f64 (-.f64 lambda1 lambda2))
	3.8b	(cos.f64 (-.f64 lambda1 lambda2))

series1.5s (9.4%)

Counts

1 → 48

Calls

1 calls:

1.5s	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`log-prod_binary64`
6×	`log-pow_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

2.0ms

(log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

391×	`fma-neg_binary64`
360×	`times-frac_binary64`
347×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
282×	`associate-/r*_binary64`

Counts

71 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	2576
1	521	2109
2	1872	2068
3	4813	2068
4	4996	2068

prune793.0ms (5.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	368	10	378

Error

0.2b

Counts

378 → 10

Alt Table

Status	Error	Program
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	4.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	26.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (sqrt.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (cos.f64 phi1))))
✓	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (.f64 1/2 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	14.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))))))
✓	0.4b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 lambda1 (+.f64 (cos.f64 lambda2) (.f64 (.f64 1/2 (sin.f64 lambda2)) lambda1))) (sin.f64 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))

Compiler

Compiled 19205 to 4089 computations (78.7% saved)

regimes1.6s (10%)

Accuracy

Total 0.1b remaining (15%)

Threshold costs 0.1b (15%)

Counts

180 → 1

Compiler

Compiled 41069 to 22683 computations (44.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-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	22	46
1	33	46
2	46	46
3	54	46
4	59	46
5	60	46
6	60	46

end1.0ms (0%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

sample6.6s (42.7%)

Algorithm

1×

intervals

Results

4.4s	4438×	body	1024	valid
934.0ms	1774×	body	512	valid
250.0ms	112×	body	2048	valid
238.0ms	738×	body	256	valid
147.0ms	938×	body	128	valid

Compiler

Compiled 447 to 219 computations (51% saved)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Details

analyze2.7s (17.2%)

sample310.0ms (2%)

simplify34.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series48.0ms (0.3%)

rewrite13.0ms (0.1%)

simplify125.0ms (0.8%)

prune207.0ms (1.3%)

localize19.0ms (0.1%)

series590.0ms (3.8%)

rewrite1.0ms (0%)

simplify59.0ms (0.4%)

prune310.0ms (2%)

localize38.0ms (0.2%)

series30.0ms (0.2%)

rewrite3.0ms (0%)

simplify71.0ms (0.5%)

prune416.0ms (2.7%)

localize21.0ms (0.1%)

series1.5s (9.4%)

rewrite4.0ms (0%)

simplify88.0ms (0.6%)

prune793.0ms (5.1%)

regimes1.6s (10%)

simplify4.0ms (0%)

end1.0ms (0%)

sample6.6s (42.7%)

Profiling

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30