Details

analyze2.6s (17.6%)

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)

sample323.0ms (2.2%)

Algorithm

1×

intervals

Results

137.0ms	145×	body	1024	valid
31.0ms	55×	body	512	valid
17.0ms	8×	body	2048	valid
7.0ms	27×	body	128	valid
7.0ms	21×	body	256	valid

Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Status

Error

Program

▶

0.5b

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

0.6b

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

Compiler

Compiled 137 to 71 computations (48.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
✓	0.4b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	4.8b	(sin.f64 (-.f64 lambda1 lambda2))
✓	4.9b	(cos.f64 (-.f64 lambda1 lambda2))

series48.0ms (0.3%)

Counts

4 → 64

Calls

4 calls:

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

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

simplify129.0ms (0.9%)

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

prune248.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	135	14	149
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	137	14	151

Error

0.4b

Counts

151 → 14

Alt Table

Status	Error	Program
	6.1b	(+.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))))))
	23.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
	1.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (+.f64 (.f64 (cos.f64 (neg.f64 lambda2)) lambda1) (sin.f64 (neg.f64 lambda2))) (.f64 1/2 (.f64 (sin.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.9b	(+.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))))))
	10.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (-.f64 (.f64 lambda1 (*.f64 (cos.f64 lambda2) 1/2)) (sin.f64 lambda2))))))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	5.1b	(+.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))))))
	34.9b	(+.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))))))
	0.9b	(+.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))))
	37.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

Compiler

Compiled 5931 to 1681 computations (71.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	0.5b	(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	4.8b	(sin.f64 (-.f64 lambda1 lambda2))
	4.9b	(cos.f64 (-.f64 lambda1 lambda2))

series31.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

31.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

2.0ms

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

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

66 → 65

Iterations

Useful iterations: 3 (0.0ms)

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

prune460.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	191	7	198
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	198	14	212

Error

0.3b

Counts

212 → 14

Alt Table

Status	Error	Program
	6.1b	(+.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))))))
	23.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	37.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	10.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))))))
	34.9b	(+.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 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (cos.f64 phi1))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
▶	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
	0.6b	(+.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))))
	13.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))

Compiler

Compiled 7688 to 2225 computations (71.1% saved)

localize17.0ms (0.1%)

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	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
	4.8b	(sin.f64 (-.f64 lambda1 lambda2))
	4.9b	(cos.f64 (-.f64 lambda1 lambda2))

series29.0ms (0.2%)

Counts

2 → 32

Calls

2 calls:

25.0ms	(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`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

3.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
313×	`unswap-sqr_binary64`
302×	`sub-neg_binary64`

Counts

80 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1238
1	365	1161
2	1300	1111
3	4037	1107
4	5009	1107

prune529.0ms (3.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	168	13	181

Error

0.3b

Counts

181 → 13

Alt Table

Status	Error	Program
	6.1b	(+.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))))))
	23.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	37.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	10.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))))))
	34.9b	(+.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 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
▶	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	13.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	1.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 lambda2) 2) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (.f64 -3 (sin.f64 lambda2)))))) (cos.f64 phi1))))

Compiler

Compiled 6945 to 2422 computations (65.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))
✓	0.6b	(pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3)
	4.8b	(sin.f64 (-.f64 lambda1 lambda2))
	4.9b	(cos.f64 (-.f64 lambda1 lambda2))

series164.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

134.0ms	(pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3)
29.0ms	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

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

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
627×	`associate-l_binary64`
459×	`associate-+r+_binary64`
306×	`associate-+l+_binary64`
232×	`*-commutative_binary64`

Counts

144 → 134

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	5652
1	1573	5322
2	5306	5322

prune533.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	215	14	229

Error

0.3b

Counts

229 → 14

Alt Table

Status	Error	Program
	34.9b	(+.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))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.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)))) 3)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))))
	6.1b	(+.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))))))
	23.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
	37.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	13.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (exp.f64 (.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))))
	5.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (*.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 2)) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	1.3b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	10.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (cos.f64 lambda1) (sin.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	13.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))))
	1.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (.f64 (pow.f64 (cos.f64 lambda2) 2) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (.f64 -3 (sin.f64 lambda2)))))) (cos.f64 phi1))))

Compiler

Compiled 11121 to 4124 computations (62.9% saved)

regimes2.6s (17.5%)

Accuracy

Total 0.2b remaining (21%)

Threshold costs 0.2b (21%)

Counts

272 → 1

Compiler

Compiled 59346 to 34870 computations (41.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	33	50
2	36	50
3	37	50
4	37	50

end1.0ms (0%)

Compiler: Compiled 34 to 22 computations (35.3% saved)

sample6.8s (45.7%)

Algorithm

1×

intervals

Results

4.5s	4400×	body	1024	valid
935.0ms	1777×	body	512	valid
285.0ms	124×	body	2048	valid
251.0ms	743×	body	256	valid
150.0ms	956×	body	128	valid

Compiler

Compiled 625 to 300 computations (52% 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

analyze2.6s (17.6%)

sample323.0ms (2.2%)

simplify34.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series48.0ms (0.3%)

rewrite12.0ms (0.1%)

simplify129.0ms (0.9%)

prune248.0ms (1.7%)

localize19.0ms (0.1%)

series31.0ms (0.2%)

rewrite2.0ms (0%)

simplify66.0ms (0.4%)

prune460.0ms (3.1%)

localize17.0ms (0.1%)

series29.0ms (0.2%)

rewrite7.0ms (0%)

simplify69.0ms (0.5%)

prune529.0ms (3.6%)

localize19.0ms (0.1%)

series164.0ms (1.1%)

rewrite5.0ms (0%)

simplify96.0ms (0.6%)

prune533.0ms (3.6%)

regimes2.6s (17.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample6.8s (45.7%)

Profiling

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