Details

analyze2.7s (18%)

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)

sample7.8s (51.8%)

Results

5.5s	4648×	body	1024	valid
1.2s	1742×	body	512	valid
363.0ms	139×	body	2048	valid
338.0ms	742×	body	256	valid
296.0ms	985×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify33.0ms (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

prune3.0ms (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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(+.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))))

Compiler

Compiled 89 to 43 computations (51.7% saved)

localize15.0ms (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)))
✓	0.5b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	4.1b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.4b	(sin.f64 (-.f64 lambda1 lambda2))

series49.0ms (0.3%)

Counts

4 → 64

Calls

4 calls:

31.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
8.0ms	(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
6.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite14.0ms (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×	`cos-sum_binary64`

Counts

4 → 65

Calls

4 calls:

6.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.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)))

simplify124.0ms (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	4591	2292
5	4928	2292

prune216.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	137	12	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Error

0.6b

Counts

150 → 12

Alt Table

Status	Error	Program
	0.8b	(+.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))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (cos.f64 phi1))))
	0.8b	(+.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))))))
	29.6b	(+.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))))))
	1.3b	(+.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 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	17.8b	(+.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))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	1.0b	(+.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))))))
	0.8b	(+.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))))

Compiler

Compiled 5717 to 1569 computations (72.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
	0.5b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
	4.1b	(cos.f64 (-.f64 lambda1 lambda2))

series18.0ms (0.1%)

Counts

2 → 32

Calls

2 calls:

9.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
3.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
506×	`sub-neg_binary64`
347×	`fma-def_binary64`
299×	`cancel-sign-sub-inv_binary64`
298×	`*-commutative_binary64`

Counts

73 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1026
1	359	934
2	1092	892
3	2224	860
4	4090	860
5	4641	860
6	4967	860

prune399.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	184	11	195

Error

0.1b

Counts

195 → 11

Alt Table

Status	Error	Program
	0.8b	(+.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))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2)))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	1.0b	(+.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))))))
	0.8b	(+.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))))))
	29.6b	(+.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))))))
	1.3b	(+.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))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	17.8b	(+.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))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.8b	(+.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))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))

Compiler

Compiled 7369 to 1936 computations (73.7% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
✓	0.3b	(.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2)))
✓	0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))

series51.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

30.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2)))
21.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log_binary64`
7×	`prod-exp_binary64`
7×	`add-cbrt-cube_binary64`
4×	`pow1_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2)))
3.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-neg_binary64`
618×	`fma-def_binary64`
458×	`*-commutative_binary64`
438×	`cancel-sign-sub-inv_binary64`
295×	`sub-neg_binary64`

Counts

79 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1526
1	455	1360
2	1470	1285
3	3683	1281
4	4971	1281

prune450.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	193	10	203

Error

0.1b

Counts

203 → 10

Alt Table

Status	Error	Program
	4.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
▶	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	29.6b	(+.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))))))
	1.3b	(+.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))))))
	3.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.0b	(+.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))))))
	0.8b	(+.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))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))

Compiler

Compiled 11524 to 3438 computations (70.2% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
	0.3b	(.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2)))
✓	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))
✓	0.8b	(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))))

series39.0ms (0.3%)

Counts

2 → 72

Calls

2 calls:

20.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))))
19.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`log-pow_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))))
0.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

563×	`sub-neg_binary64`
500×	`fma-neg_binary64`
390×	`*-commutative_binary64`
343×	`associate-+l+_binary64`
266×	`associate-+r+_binary64`

Counts

100 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1617
1	220	1551
2	601	1499
3	1910	1477
4	4239	1477
5	4988	1477
6	4963	1477

prune424.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	155	5	160
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
	3.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (log.f64 (exp.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.8b	(+.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))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 phi2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 phi2) (cos.f64 phi1)))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	4.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	29.6b	(+.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 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1))))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	13.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (exp.f64 (log.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 phi2) (cos.f64 phi1)))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.0b	(+.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))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))) (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 lambda2) (cos.f64 phi1)))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)) (.f64 1/2 (.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))))))

Compiler

Compiled 9389 to 2705 computations (71.2% saved)

regimes2.0s (13.5%)

Accuracy

Total -0.2b remaining (-93.4%)

Threshold costs -0.2b (-93.4%)

Counts

176 → 1

Compiler

Compiled 53928 to 30537 computations (43.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	33	54
2	43	54
3	49	54
4	53	54
5	54	54
6	54	54

end306.0ms (2%)

Compiler: Compiled 629 to 326 computations (48.2% 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 (18%)

sample7.8s (51.8%)

simplify33.0ms (0.2%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series49.0ms (0.3%)

rewrite14.0ms (0.1%)

simplify124.0ms (0.8%)

prune216.0ms (1.4%)

localize23.0ms (0.2%)

series18.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify87.0ms (0.6%)

prune399.0ms (2.6%)

localize36.0ms (0.2%)

series51.0ms (0.3%)

rewrite11.0ms (0.1%)

simplify68.0ms (0.5%)

prune450.0ms (3%)

localize37.0ms (0.2%)

series39.0ms (0.3%)

rewrite3.0ms (0%)

simplify99.0ms (0.7%)

prune424.0ms (2.8%)

regimes2.0s (13.5%)

simplify4.0ms (0%)

end306.0ms (2%)

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