Details

analyze3.7s (17.8%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample10.5s (50.4%)

Results

8.1s	5673×	body	1024	valid
1.2s	1471×	body	512	valid
754.0ms	255×	body	2048	valid
308.0ms	537×	body	256	valid
97.0ms	320×	body	128	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 50 to 36 computations (28% saved)

preprocess78.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1299×	`fma-def_binary64`
458×	`fma-neg_binary64`
236×	`cancel-sign-sub-inv_binary64`
181×	`distribute-rgt-in_binary64`
160×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	319
1	181	319
2	307	319
3	402	319
4	466	319
5	670	319
6	894	319
7	1289	319
8	2073	319
9	3037	319
10	3654	319
11	4561	319
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

47×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)

Compiler

Compiled 88 to 55 computations (37.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))))
✓	2.9b	(cos.f64 (-.f64 lambda2 lambda1))

series76.0ms (0.4%)

Counts

4 → 164

Calls

45 calls:

5.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))	lambda2	-inf
3.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))	lambda1	inf
3.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))	lambda2	inf
3.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))	phi2	inf
3.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))	phi1	-inf

rewrite76.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

355×	`log1p-udef_binary64`
195×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	362	77
2	4849	77

Stop Event

1×	node limit

Counts

4 → 81

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

573×	`cancel-sign-sub-inv_binary64`
568×	`fma-def_binary64`
442×	`*-commutative_binary64`
334×	`sub-neg_binary64`
248×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	4331
1	434	4272
2	1451	4154
3	4577	4154

Stop Event

1×	node limit

Counts

245 → 133

prune175.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	118	15	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	15	134

Error

3.6b

Counts

134 → 15

Alt Table

Status	Error	Program
	15.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	15.3b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	14.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 1))) R)
	14.8b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	46.2b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	14.9b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	39.5b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	14.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))))) R)
▶	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
	14.9b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))) R)
	15.4b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log1p.f64 (expm1.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
	14.9b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2) R)

Compiler

Compiled 4660 to 1616 computations (65.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
✓	0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))

series124.0ms (0.6%)

Counts

4 → 180

Calls

45 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))	lambda1	inf
8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))	phi1	inf
7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))	phi2	-inf
7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))	phi1	-inf
6.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))	lambda2	inf

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

226×	`add-sqr-sqrt_binary64`
207×	`log1p-expm1-u_binary64`
207×	`expm1-log1p-u_binary64`
206×	`add-log-exp_binary64`
205×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	109
1	427	79

Stop Event

1×	node limit

Counts

4 → 75

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

401×	`fma-neg_binary64`
349×	`associate-r_binary64`
322×	`distribute-rgt-neg-in_binary64`
315×	`associate--l+_binary64`
304×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	6296
1	674	6240
2	2497	6059

Stop Event

1×	node limit

Counts

255 → 132

prune220.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	132	15	147

Error

3.6b

Counts

147 → 15

Alt Table

Status	Error	Program
	15.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	15.3b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	14.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 1))) R)
	14.8b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	46.2b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	14.9b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	39.5b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
▶	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1))))))) R)
	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log1p.f64 (expm1.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	14.9b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))) R)
	15.4b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	14.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))))) R)
	14.9b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2) R)

Compiler

Compiled 5323 to 1885 computations (64.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1))))))) R)
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))))))
✓	2.6b	(log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))

series1.8s (8.7%)

Counts

4 → 180

Calls

45 calls:

152.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))))	lambda2	-inf
151.0ms	(log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))	lambda2	inf
149.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))))	lambda2	inf
146.0ms	(log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))	lambda2	-inf
142.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1)))))	lambda1	inf

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`add-sqr-sqrt_binary64`
220×	`add-log-exp_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
218×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	109
1	462	109

Stop Event

1×	node limit

Counts

4 → 72

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

401×	`fma-neg_binary64`
350×	`associate-r_binary64`
322×	`distribute-rgt-neg-in_binary64`
315×	`associate--l+_binary64`
304×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	6728
1	679	6240
2	2522	6059

Stop Event

1×	node limit

Counts

252 → 125

prune215.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	125	15	140

Error

3.5b

Counts

140 → 15

Alt Table

Status	Error	Program
	15.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	4.7b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) 3)
	14.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 1))) R)
	14.8b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
▶	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	4.1b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 2) R)
	14.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))))) R)
	4.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) 1) R)
	14.9b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))) R)
	46.2b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	4.7b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 3) R)
✓	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1))))))) R)
	4.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	33.6b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) 2)

Compiler

Compiled 5445 to 1856 computations (65.9% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))))))
✓	30.1b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))

series46.0ms (0.2%)

Counts

3 → 96

Calls

24 calls:

6.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)	lambda2	inf
4.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)	lambda1	-inf
4.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)	lambda2	-inf
4.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)	lambda1	inf
4.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)	lambda2	0

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
208×	`add-cbrt-cube_binary64`
206×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	55
1	451	45

Stop Event

1×	node limit

Counts

3 → 78

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-r_binary64`
589×	`associate-l_binary64`
420×	`fma-def_binary64`
290×	`cancel-sign-sub-inv_binary64`
266×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	2572
1	271	2556
2	1019	2484
3	4904	2484

Stop Event

1×	node limit

Counts

174 → 112

prune256.0ms (1.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	149	15	164

Error

3.5b

Counts

164 → 15

Alt Table

Status	Error	Program
	15.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	4.7b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) 3)
	14.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 1))) R)
	14.8b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
✓	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	4.1b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 2) R)
	14.7b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))))) R)
	4.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) 1) R)
	14.9b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))) R)
	46.2b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	4.7b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 3) R)
✓	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1))))))) R)
	4.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	33.6b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) 2)

Compiler

Compiled 5480 to 2070 computations (62.2% saved)

regimes2.6s (12.3%)

Accuracy

Total 0.3b remaining (7.5%)

Threshold costs 0.3b (7.5%)

Counts

191 → 1

Compiler

Compiled 58568 to 39502 computations (32.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	30	39

Stop Event

1×

saturated

end368.0ms (1.8%)

Stop Event

1×

fuel

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 754 to 469 computations (37.8% saved)

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Details

analyze3.7s (17.8%)

sample10.5s (50.4%)

preprocess78.0ms (0.4%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series76.0ms (0.4%)

rewrite76.0ms (0.4%)

simplify101.0ms (0.5%)

prune175.0ms (0.8%)

localize23.0ms (0.1%)

series124.0ms (0.6%)

rewrite39.0ms (0.2%)

simplify108.0ms (0.5%)

prune220.0ms (1.1%)

localize27.0ms (0.1%)

series1.8s (8.7%)

rewrite42.0ms (0.2%)

simplify108.0ms (0.5%)

prune215.0ms (1%)

localize27.0ms (0.1%)

series46.0ms (0.2%)

rewrite36.0ms (0.2%)

simplify73.0ms (0.4%)

prune256.0ms (1.2%)

regimes2.6s (12.3%)

simplify2.0ms (0%)

end368.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29