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 (53.1%)

Results

5.5s	4564×	body	1024	valid
1.3s	1820×	body	512	valid
344.0ms	762×	body	256	valid
298.0ms	114×	body	2048	valid
244.0ms	996×	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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(+.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))
✓	5.8b	(sin.f64 (-.f64 lambda1 lambda2))
✓	5.9b	(cos.f64 (-.f64 lambda1 lambda2))

series99.0ms (0.7%)

Counts

4 → 64

Calls

4 calls:

84.0ms	(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)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite61.0ms (0.4%)

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:

53.0ms	(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)))

simplify147.0ms (1%)

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

prune361.0ms (2.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	132	17	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	17	150

Error

0.8b

Counts

150 → 17

Alt Table

Status	Error	Program
	13.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2))) -1/2 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))))
	7.4b	(+.f64 lambda1 (cbrt.f64 (.f64 (.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))) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	31.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.1b	(+.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))))
▶	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)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (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))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (.f64 (*.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	1.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	13.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (log.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	13.9b	(+.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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	1.4b	(+.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))))))
	1.1b	(+.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))))))
	5.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	7.3b	(+.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))))
	12.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))) (cos.f64 phi1))))
	1.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 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))))))))

Compiler

Compiled 6203 to 1795 computations (71.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.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)))) (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))
	5.9b	(cos.f64 (-.f64 lambda1 lambda2))

series27.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

14.0ms

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

13.0ms

(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)))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 25

Calls

2 calls:

5.0ms

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

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

465×	`cancel-sign-sub-inv_binary64`
400×	`fma-neg_binary64`
355×	`unsub-neg_binary64`
288×	`sub-neg_binary64`
271×	`associate-l_binary64`

Counts

97 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	3248
1	226	3121
2	659	3106
3	1905	3101
4	4115	3099
5	4906	3099

prune538.0ms (3.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	156	15	171

Error

0.1b

Counts

171 → 15

Alt Table

Status	Error	Program
	13.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2))) -1/2 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))))
	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)))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
	1.8b	(+.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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2)))) (.f64 (cos.f64 phi2) (.f64 (sin.f64 (neg.f64 lambda2)) lambda1)))))
	1.4b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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)))) (cbrt.f64 (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))))) (cbrt.f64 (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))))))
	5.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	7.4b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
	1.1b	(+.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) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	31.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.1b	(+.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))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (-.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))))
▶	0.3b	(+.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) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	1.1b	(+.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))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (-.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))))
	13.9b	(+.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))))))
	13.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (/.f64 (exp.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (exp.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

Compiler

Compiled 6825 to 1729 computations (74.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series90.0ms (0.6%)

Counts

3 → 104

Calls

3 calls:

64.0ms

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

15.0ms

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

11.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

3.0ms

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

0.0ms

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

0.0ms

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

simplify149.0ms (1%)

Algorithm

1×	egg-herbie

Rules

756×	`cancel-sign-sub-inv_binary64`
603×	`sub-neg_binary64`
440×	`associate-+l+_binary64`
421×	`associate--l+_binary64`
220×	`distribute-rgt-neg-in_binary64`

Counts

144 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	5476
1	581	5020
2	1890	4940
3	4631	4940
4	5316	4940

prune464.0ms (3.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	155	15	170

Error

0.1b

Counts

170 → 15

Alt Table

Status	Error	Program
	13.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2))) -1/2 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))))
▶	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)))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
	1.4b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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)))) (cbrt.f64 (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))))) (cbrt.f64 (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))))))
	5.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	7.4b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
	1.1b	(+.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) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	31.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.1b	(+.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))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (-.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))))
	1.8b	(+.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 (cos.f64 phi2) (cos.f64 lambda2)) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) lambda1)) (cos.f64 phi1)))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (-.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))))
✓	0.3b	(+.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) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	1.1b	(+.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))))))
	13.9b	(+.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))))))
	13.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (/.f64 (exp.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (exp.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

Compiler

Compiled 7596 to 1761 computations (76.8% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))
✓	0.5b	(fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))
✓	0.6b	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
	5.9b	(cos.f64 (-.f64 lambda1 lambda2))

series53.0ms (0.4%)

Counts

3 → 80

Calls

3 calls:

29.0ms	(fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))
20.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
4.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

3.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))
0.0ms	(fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`cancel-sign-sub-inv_binary64`
495×	`fma-neg_binary64`
371×	`unswap-sqr_binary64`
282×	`distribute-rgt-neg-in_binary64`
240×	`associate-r_binary64`

Counts

138 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2419
1	582	2282
2	2154	2260
3	4561	2254
4	4976	2254

prune487.0ms (3.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	179	14	193

Error

0.1b

Counts

193 → 14

Alt Table

Status	Error	Program
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))))
	13.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2))) -1/2 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))))
	1.4b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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)))) (cbrt.f64 (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))))) (cbrt.f64 (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))))))
	5.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	7.4b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
	1.1b	(+.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) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	31.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	1.1b	(+.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))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (-.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))))
	1.8b	(+.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 (cos.f64 phi2) (cos.f64 lambda2)) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) lambda1)) (cos.f64 phi1)))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (-.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))))
✓	0.3b	(+.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) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	13.9b	(+.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))))))
	13.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (/.f64 (exp.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (exp.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

Compiler

Compiled 7633 to 2150 computations (71.8% saved)

regimes1.1s (7.6%)

Accuracy

Total 0.1b remaining (51.6%)

Threshold costs 0.1b (51.6%)

Counts

129 → 1

Compiler

Compiled 33075 to 17776 computations (46.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-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	20	52
1	30	52
2	40	52
3	46	52
4	50	52
5	51	52
6	51	52

end296.0ms (2%)

Compiler: Compiled 594 to 315 computations (47% 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 (53.1%)

simplify33.0ms (0.2%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series99.0ms (0.7%)

rewrite61.0ms (0.4%)

simplify147.0ms (1%)

prune361.0ms (2.5%)

localize23.0ms (0.2%)

series27.0ms (0.2%)

rewrite6.0ms (0%)

simplify114.0ms (0.8%)

prune538.0ms (3.7%)

localize24.0ms (0.2%)

series90.0ms (0.6%)

rewrite6.0ms (0%)

simplify149.0ms (1%)

prune464.0ms (3.2%)

localize31.0ms (0.2%)

series53.0ms (0.4%)

rewrite7.0ms (0%)

simplify89.0ms (0.6%)

prune487.0ms (3.3%)

regimes1.1s (7.6%)

simplify4.0ms (0%)

end296.0ms (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