Details

analyze2.7s (18.3%)

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 (51.6%)

Results

5.5s	4534×	body	1024	valid
1.3s	1825×	body	512	valid
344.0ms	755×	body	256	valid
304.0ms	113×	body	2048	valid
260.0ms	1029×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify32.0ms (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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.0b	(+.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))))
▶	1.0b	(+.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

1.0b

(+.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))))

▶

1.0b

(+.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)

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))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	3.2b	(cos.f64 (-.f64 lambda1 lambda2))
✓	3.2b	(sin.f64 (-.f64 lambda1 lambda2))

series46.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

27.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
10.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

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

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
723×	`fma-def_binary64`
670×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`
219×	`distribute-lft-neg-in_binary64`

Counts

185 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	4873
1	598	4011
2	1754	3815
3	4238	3804
4	4942	3804

prune260.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	148	14	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	14	164

Error

0.7b

Counts

164 → 14

Alt Table

Status	Error	Program
	40.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	17.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (exp.f64 (cos.f64 phi1)) (exp.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.3b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) (*.f64 lambda1 lambda1)) -1/2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 1/2 (.f64 lambda1 (.f64 lambda1 (sin.f64 lambda2))) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	39.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))))))))
▶	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	7.0b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	4.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))

Compiler

Compiled 6717 to 1838 computations (72.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
	3.2b	(cos.f64 (-.f64 lambda1 lambda2))

series24.0ms (0.2%)

Counts

2 → 56

Calls

2 calls:

14.0ms

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

10.0ms

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms

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

0.0ms

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

simplify143.0ms (1%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-neg_binary64`
509×	`distribute-rgt-neg-in_binary64`
421×	`distribute-lft-neg-in_binary64`
356×	`*-commutative_binary64`
259×	`associate-l_binary64`

Counts

86 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	2942
1	239	2701
2	623	2681
3	1637	2658
4	2954	2658
5	4832	2658
6	4949	2658
7	4899	2658

prune358.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	165	10	175

Error

0.1b

Counts

175 → 10

Alt Table

Status	Error	Program
	17.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (exp.f64 (cos.f64 phi1)) (exp.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.3b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	4.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	7.0b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (cbrt.f64 (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 7020 to 1649 computations (76.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓	0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series92.0ms (0.6%)

Counts

3 → 104

Calls

3 calls:

65.0ms

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

18.0ms

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

9.0ms

(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 48

Calls

3 calls:

4.0ms

(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

3.0ms

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

0.0ms

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

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

803×	`cancel-sign-sub-inv_binary64`
608×	`fma-neg_binary64`
307×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
259×	`distribute-rgt-neg-in_binary64`

Counts

152 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	6072
1	655	5224
2	2205	5149
3	4528	5147
4	4985	5147

prune574.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	17.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (exp.f64 (cos.f64 phi1)) (exp.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.3b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	12.5b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	7.0b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	4.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))

Compiler

Compiled 7931 to 1752 computations (77.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
✓	0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
✓	3.9b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series98.0ms (0.7%)

Counts

3 → 120

Calls

3 calls:

67.0ms

(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

19.0ms

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

11.0ms

(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`

Counts

3 → 43

Calls

3 calls:

5.0ms

(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

1.0ms

(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

0.0ms

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

simplify175.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

800×	`cancel-sign-sub-inv_binary64`
527×	`fma-neg_binary64`
307×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
245×	`distribute-rgt-neg-in_binary64`

Counts

163 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	6151
1	613	5309
2	2012	5234
3	4303	5226
4	4979	5226
5	4969	5226

prune373.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	163	11	174

Error

0.1b

Counts

174 → 11

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
	5.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	17.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (exp.f64 (cos.f64 phi1)) (exp.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.3b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	4.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
	12.5b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	7.0b	(+.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))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (cbrt.f64 (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 7811 to 1683 computations (78.5% saved)

regimes1.7s (11.5%)

Accuracy

Total 0.1b remaining (57.1%)

Threshold costs 0.1b (57.1%)

Counts

197 → 1

Compiler

Compiled 49119 to 27219 computations (44.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-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	24	60
1	38	60
2	48	60
3	54	60
4	58	60
5	59	60
6	59	60

end223.0ms (1.5%)

Compiler: Compiled 537 to 247 computations (54% 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 (18.3%)

sample7.8s (51.6%)

simplify32.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series46.0ms (0.3%)

rewrite17.0ms (0.1%)

simplify124.0ms (0.8%)

prune260.0ms (1.7%)

localize23.0ms (0.2%)

series24.0ms (0.2%)

rewrite5.0ms (0%)

simplify143.0ms (1%)

prune358.0ms (2.4%)

localize22.0ms (0.1%)

series92.0ms (0.6%)

rewrite11.0ms (0.1%)

simplify142.0ms (0.9%)

prune574.0ms (3.8%)

localize26.0ms (0.2%)

series98.0ms (0.7%)

rewrite9.0ms (0.1%)

simplify175.0ms (1.2%)

prune373.0ms (2.5%)

regimes1.7s (11.5%)

simplify3.0ms (0%)

end223.0ms (1.5%)

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