Details

analyze2.8s (15.3%)

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)

sample8.8s (48.2%)

Results

6.7s	4610×	body	1024	valid
1.2s	1808×	body	512	valid
343.0ms	727×	body	256	valid
277.0ms	111×	body	2048	valid
242.0ms	1000×	body	128	valid

Compiler

Compiled 50 to 30 computations (40% saved)

preprocess16.0ms (0.1%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	224
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 24 to 14 computations (41.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	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 72 to 42 computations (41.7% 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))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	2.9b	(cos.f64 (-.f64 lambda1 lambda2))
✓	3.0b	(sin.f64 (-.f64 lambda1 lambda2))

series43.0ms (0.2%)

Counts

4 → 112

Calls

36 calls:

3.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi1	inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	lambda1	-inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi2	-inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi2	inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	lambda2	inf

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`expm1-udef_binary64`
297×	`log1p-udef_binary64`
163×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	285	57
2	3344	57

Stop Event

1×	node limit

Counts

4 → 90

simplify459.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1762×	`sqr-pow_binary64`
860×	`pow-sqr_binary64`
112×	`cube-prod_binary64`
112×	`cube-mult_binary64`
112×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	2748
1	176	2748
2	204	2748
3	240	2748
4	295	2748
5	358	2748
6	429	2748
7	511	2748
8	602	2748
9	704	2748
10	815	2748
11	937	2748
12	1068	2748
13	1210	2748
14	1361	2748
15	1523	2748
16	1694	2748
17	1876	2748
18	2067	2748
19	2269	2748
20	2285	2748
21	2293	2748
22	2293	2748
23	2500	2748
24	2714	2748
25	2945	2748
26	3187	2748
27	3438	2748
28	3700	2748
29	3971	2748
30	4041	2748
31	4049	2748
32	4049	2748
33	4322	2748
34	4604	2748
35	4903	2748

Stop Event

1×	node limit

Counts

202 → 149

prune191.0ms (1%)

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

0.2b

Counts

150 → 12

Alt Table

Status	Error	Program
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (+.f64 1 (expm1.f64 (cos.f64 phi1))) (pow.f64 (exp.f64 (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.8b	(+.f64 lambda1 (cbrt.f64 (pow.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))))) 3)))
	15.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 3) 1/3)))
	0.8b	(+.f64 lambda1 (pow.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)))))) 3))
	0.4b	(+.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 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
▶	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 2)) (cbrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	11.7b	(+.f64 lambda1 (log.f64 (exp.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 5402 to 1514 computations (72% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
	2.9b	(cos.f64 (-.f64 lambda1 lambda2))

series47.0ms (0.3%)

Counts

2 → 84

Calls

21 calls:

5.0ms	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))	phi2	-inf
5.0ms	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))	phi2	inf
5.0ms	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))	lambda1	-inf
4.0ms	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))	lambda2	-inf
4.0ms	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))	lambda2	inf

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

395×	`log1p-udef_binary64`
218×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
202×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	388	64
2	4411	64

Stop Event

1×	node limit

Counts

2 → 29

simplify547.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1699×	`sqr-pow_binary64`
826×	`pow-sqr_binary64`
96×	`cube-prod_binary64`
96×	`cube-mult_binary64`
96×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	3043
1	151	3043
2	178	3043
3	208	3043
4	251	3043
5	300	3043
6	355	3043
7	418	3043
8	488	3043
9	566	3043
10	651	3043
11	744	3043
12	844	3043
13	952	3043
14	1067	3043
15	1190	3043
16	1320	3043
17	1458	3043
18	1603	3043
19	1756	3043
20	1916	3043
21	2084	3043
22	2259	3043
23	2271	3043
24	2277	3043
25	2277	3043
26	2457	3043
27	2641	3043
28	2839	3043
29	3044	3043
30	3257	3043
31	3477	3043
32	3705	3043
33	3940	3043
34	3999	3043
35	4005	3043
36	4005	3043
37	4241	3043
38	4484	3043
39	4740	3043

Stop Event

1×	node limit

Counts

113 → 53

prune321.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	141	12	153

Error

0.1b

Counts

153 → 12

Alt Table

Status	Error	Program
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (+.f64 1 (expm1.f64 (cos.f64 phi1))) (pow.f64 (exp.f64 (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.8b	(+.f64 lambda1 (cbrt.f64 (pow.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))))) 3)))
	15.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 3) 1/3)))
	0.8b	(+.f64 lambda1 (pow.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)))))) 3))
	0.4b	(+.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 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 2)) (cbrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	11.7b	(+.f64 lambda1 (log.f64 (exp.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 5969 to 1587 computations (73.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series78.0ms (0.4%)

Counts

3 → 104

Calls

30 calls:

6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi1	-inf
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	lambda1	-inf
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi2	-inf
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi2	inf
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi1	inf

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`log1p-udef_binary64`
212×	`add-sqr-sqrt_binary64`
196×	`log1p-expm1-u_binary64`
196×	`expm1-log1p-u_binary64`
194×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	85
1	380	65
2	4213	65

Stop Event

1×	node limit

Counts

3 → 48

simplify621.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1646×	`sqr-pow_binary64`
708×	`pow-sqr_binary64`
108×	`cube-mult_binary64`
108×	`unpow3_binary64`
104×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	4272
1	235	4272
2	279	4272
3	328	4272
4	396	4272
5	473	4272
6	558	4272
7	654	4272
8	759	4272
9	875	4272
10	1000	4272
11	1136	4272
12	1281	4272
13	1437	4272
14	1602	4272
15	1778	4272
16	1963	4272
17	2159	4272
18	2364	4272
19	2380	4272
20	2388	4272
21	2388	4272
22	2600	4272
23	2817	4272
24	3053	4272
25	3298	4272
26	3554	4272
27	3819	4272
28	4095	4272
29	4380	4272
30	4396	4272
31	4404	4272
32	4404	4272
33	4696	4272
34	4993	4272

Stop Event

1×	node limit

Counts

152 → 95

prune302.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	131	12	143

Error

0.1b

Counts

143 → 12

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (+.f64 1 (expm1.f64 (cos.f64 phi1))) (pow.f64 (exp.f64 (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.8b	(+.f64 lambda1 (cbrt.f64 (pow.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))))) 3)))
	15.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 3) 1/3)))
	0.8b	(+.f64 lambda1 (pow.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)))))) 3))
	0.4b	(+.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 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 2)) (cbrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	11.7b	(+.f64 lambda1 (log.f64 (exp.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 6151 to 1652 computations (73.1% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
✓	0.3b	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
	2.9b	(cos.f64 (-.f64 lambda1 lambda2))

series61.0ms (0.3%)

Counts

2 → 96

Calls

24 calls:

6.0ms	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))	lambda1	0
6.0ms	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))	phi2	0
5.0ms	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))	lambda2	0
4.0ms	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))	lambda2	inf
4.0ms	(expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))	lambda1	-inf

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

410×	`log1p-udef_binary64`
226×	`add-sqr-sqrt_binary64`
213×	`expm1-log1p-u_binary64`
212×	`log1p-expm1-u_binary64`
209×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	409	59
2	4583	59

Stop Event

1×	node limit

Counts

2 → 30

simplify241.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1271×	`sqr-pow_binary64`
829×	`pow-sqr_binary64`
81×	`cube-mult_binary64`
81×	`unpow3_binary64`
72×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	184	4020
1	290	4020
2	356	4020
3	447	4020
4	576	4020
5	737	4020
6	955	4020
7	1255	4020
8	1700	4020
9	2384	4020
10	3524	4020
11	3560	4020
12	3576	4020
13	3576	4020

Stop Event

1×	node limit

Counts

126 → 65

prune417.0ms (2.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	153	12	165

Error

0.0b

Counts

165 → 12

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (.f64 (+.f64 1 (expm1.f64 (cos.f64 phi1))) (pow.f64 (exp.f64 (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.8b	(+.f64 lambda1 (cbrt.f64 (pow.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))))) 3)))
	15.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 3) 1/3)))
	0.8b	(+.f64 lambda1 (pow.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)))))) 3))
	0.4b	(+.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 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log1p.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) 3) 1) (+.f64 (.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (+.f64 1 (.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) 1)))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) 2)) (cbrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	11.7b	(+.f64 lambda1 (log.f64 (exp.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 7463 to 1972 computations (73.6% saved)

regimes2.8s (15.2%)

Accuracy

Total 0.1b remaining (55.2%)

Threshold costs 0.1b (55.2%)

Counts

120 → 1

Compiler

Compiled 27461 to 16397 computations (40.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54

Stop Event

1×

saturated

end274.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 505 to 281 computations (44.4% saved)

Details

analyze2.8s (15.3%)

sample8.8s (48.2%)

preprocess16.0ms (0.1%)

simplify4.0ms (0%)

prune2.0ms (0%)

localize15.0ms (0.1%)

series43.0ms (0.2%)

rewrite51.0ms (0.3%)

simplify459.0ms (2.5%)

prune191.0ms (1%)

localize24.0ms (0.1%)

series47.0ms (0.3%)

rewrite45.0ms (0.2%)

simplify547.0ms (3%)

prune321.0ms (1.7%)

localize23.0ms (0.1%)

series78.0ms (0.4%)

rewrite49.0ms (0.3%)

simplify621.0ms (3.4%)

prune302.0ms (1.6%)

localize27.0ms (0.1%)

series61.0ms (0.3%)

rewrite48.0ms (0.3%)

simplify241.0ms (1.3%)

prune417.0ms (2.3%)

regimes2.8s (15.2%)

simplify1.0ms (0%)

end274.0ms (1.5%)

Profiling