Details

analyze4.1s (20.6%)

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
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)

sample10.3s (50.9%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

7.9s	5711×	body	1024	valid
1.2s	1477×	body	512	valid
709.0ms	240×	body	2048	valid
270.0ms	503×	body	256	valid
95.0ms	325×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify11.0ms (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

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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.4b	(.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)
▶	14.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Status

Error

Program

14.4b

(*.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)

▶

14.4b

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

Compiler

Compiled 136 to 89 computations (34.6% saved)

localize20.0ms (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 lambda1 lambda2)))
✓	0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
✓	0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	2.3b	(cos.f64 (-.f64 lambda1 lambda2))

series58.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

34.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`
176×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	355	56

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

34.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
34.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
34.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
34.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

743×	`cancel-sign-sub-inv_binary64`
666×	`fma-def_binary64`
310×	`distribute-rgt-neg-in_binary64`
292×	`distribute-lft-neg-in_binary64`
287×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2801
1	550	2755
2	1829	2594

Stop Event

1×	node limit

Counts

194 → 145

prune212.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	130	15	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	15	147

Error

3.1b

Counts

147 → 15

Alt Table

Status	Error	Program
	14.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))) R)
	14.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2) R)
	14.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	15.0b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 3) R)
	14.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	14.6b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1) R)
	14.4b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
▶	3.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	14.4b	(.f64 (pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3) R)
	3.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	14.6b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	14.6b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
	3.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) R)
	14.6b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)

Compiler

Compiled 5274 to 1869 computations (64.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series124.0ms (0.6%)

Counts

3 → 156

Calls

3 calls:

67.0ms

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

43.0ms

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

14.0ms

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

rewrite31.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
225×	`log1p-expm1-u_binary64`
225×	`expm1-log1p-u_binary64`
223×	`add-cbrt-cube_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	101
1	460	71

Stop Event

1×	node limit

Counts

3 → 45

Calls

3 calls:

30.0ms

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

30.0ms

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

30.0ms

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

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

906×	`cancel-sign-sub-inv_binary64`
343×	`fma-neg_binary64`
318×	`associate-r_binary64`
292×	`associate--l+_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	5964
1	578	5916
2	2161	5759

Stop Event

1×	node limit

Counts

201 → 86

prune198.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	117	17	134

Error

3.1b

Counts

134 → 17

Alt Table

Status	Error	Program
	44.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R) 3))
	14.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2) R)
	40.2b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)) 2)
	14.4b	(.f64 (pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3) R)
	15.1b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)) 3)
	14.5b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	3.4b	(.f64 (acos.f64 (+.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi2)) (sin.f64 phi1))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
▶	3.4b	(.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
	28.6b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)))
	14.4b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))) R)
	14.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	14.6b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	14.6b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
	14.5b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	14.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	14.6b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)

Compiler

Compiled 5014 to 1760 computations (64.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)
	0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
✓	0.7b	(acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series127.0ms (0.6%)

Counts

3 → 156

Calls

3 calls:

84.0ms

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

33.0ms

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

10.0ms

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

rewrite40.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	109
1	425	109

Stop Event

1×	node limit

Counts

3 → 57

Calls

3 calls:

37.0ms

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

37.0ms

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

37.0ms

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

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
726×	`cancel-sign-sub-inv_binary64`
429×	`*-commutative_binary64`
250×	`distribute-rgt-neg-in_binary64`
236×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	6320
1	401	6291
2	1465	5847

Stop Event

1×	node limit

Counts

213 → 95

prune219.0ms (1.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	117	11	128
Fresh	11	5	16
Picked	1	0	1
Done	0	0	0
Total	129	16	145

Error

3.0b

Counts

145 → 16

Alt Table

Status	Error	Program
	3.5b	(.f64 (acos.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	44.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R) 3))
	3.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2) R)
	3.4b	(.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (log.f64 (pow.f64 (exp.f64 (sin.f64 phi2)) (sin.f64 phi1))))) R)
	19.5b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.8b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))) R)
	14.6b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	33.6b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) 2)
	3.4b	(.f64 (-.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	14.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
▶	3.4b	(.f64 (pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3) R)
	15.1b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)) 3)
	14.6b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.6b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)
	3.4b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)

Compiler

Compiled 5451 to 1644 computations (69.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
✓	0.3b	(pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3)
✓	0.7b	(pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)
	0.7b	(acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series500.0ms (2.5%)

Counts

2 → 96

Calls

2 calls:

424.0ms

(pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3)

75.0ms

(pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

233×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
214×	`add-log-exp_binary64`
213×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	75
1	464	75

Stop Event

1×	node limit

Counts

2 → 35

Calls

2 calls:

32.0ms

(pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3)

32.0ms

(pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)

simplify257.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

730×	`sqr-pow_binary64`
362×	`unswap-sqr_binary64`
325×	`cube-prod_binary64`
313×	`pow-sqr_binary64`
221×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	3600
1	36	3600
2	55	3600
3	129	3600
4	287	3600
5	547	3600
6	899	3600
7	1559	3600
8	1646	3600
9	1779	3600
10	1937	3600
11	2165	3600
12	2487	3600
13	2908	3600
14	3408	3600
15	4003	3600
16	4723	3600

Stop Event

1×	node limit

Counts

131 → 39

prune204.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	94	17	111

Error

3.0b

Counts

111 → 17

Alt Table

Status	Error	Program
	3.5b	(.f64 (acos.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	44.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R) 3))
	3.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2) R)
	3.4b	(.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (log.f64 (pow.f64 (exp.f64 (sin.f64 phi2)) (sin.f64 phi1))))) R)
	19.5b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.8b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))) R)
	14.6b	(.f64 (/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (+.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (+.f64 (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	33.6b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) 2)
	3.4b	(.f64 (-.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	14.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	15.1b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)) 3)
	14.6b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.4b	(.f64 (pow.f64 (pow.f64 (pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3) 3) 1/3) R)
	3.4b	(.f64 (pow.f64 (pow.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) 3) 1/3) R)
	3.7b	(.f64 (pow.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3))) 1) 1/3) R)
	3.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.6b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)

Compiler

Compiled 4195 to 1278 computations (69.5% saved)

regimes2.9s (14.5%)

Accuracy

Total 0.3b remaining (7.6%)

Threshold costs 0.3b (7.6%)

Counts

176 → 1

Compiler

Compiled 58686 to 39820 computations (32.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	33	41

Stop Event

1×

saturated

end462.0ms (2.3%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 842 to 538 computations (36.1% 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

analyze4.1s (20.6%)

sample10.3s (50.9%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series58.0ms (0.3%)

rewrite36.0ms (0.2%)

simplify54.0ms (0.3%)

prune212.0ms (1%)

localize24.0ms (0.1%)

series124.0ms (0.6%)

rewrite31.0ms (0.2%)

simplify92.0ms (0.5%)

prune198.0ms (1%)

localize23.0ms (0.1%)

series127.0ms (0.6%)

rewrite40.0ms (0.2%)

simplify91.0ms (0.5%)

prune219.0ms (1.1%)

localize28.0ms (0.1%)

series500.0ms (2.5%)

rewrite34.0ms (0.2%)

simplify257.0ms (1.3%)

prune204.0ms (1%)

regimes2.9s (14.5%)

simplify2.0ms (0%)

end462.0ms (2.3%)

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