Details

analyze2.8s (14.8%)

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
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample5.2s (27.3%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

1.6s	6244×	body	128	valid
1.3s	784×	body	1024	valid
631.0ms	491×	body	1024	invalid
538.0ms	2449×	body	128	invalid
459.0ms	769×	body	512	valid
303.0ms	398×	body	512	invalid
225.0ms	451×	body	256	valid
77.0ms	191×	body	256	invalid
15.0ms	8×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify115.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1413×	`unsub-neg_binary64`
897×	`distribute-neg-out_binary64`
703×	`fma-def_binary64`
583×	`neg-sub0_binary64`
478×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	35	24
2	83	24
3	224	24
4	658	24
5	2038	24
6	3128	24
7	3593	24
8	4399	24
9	4364	24
10	4430	24
11	4468	24
12	5035	24

prune5.0ms (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

3.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
	34.3b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Status

Error

Program

▶

3.3b

(*.f64 R (hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

34.3b

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 169 to 97 computations (42.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
✓	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (7.2%)

Counts

4 → 180

Calls

4 calls:

862.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
486.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
23.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite70.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
307×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

4 → 77

Calls

4 calls:

69.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
69.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
69.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
69.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	331	69
2	4247	69
3	5102	69

simplify405.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1133×	`associate-r_binary64`
461×	`fma-def_binary64`
141×	`associate-l_binary64`
85×	`sub-neg_binary64`
65×	`associate-/l*_binary64`

Counts

257 → 273

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2196	44761
1	5035	44761

prune1.2s (6.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	259	14	273
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	261	14	275

Error

3.2b

Counts

275 → 14

Alt Table

Status	Error	Program
	4.4b	(.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (-.f64 phi1 phi2)))
	23.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	37.3b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (fma.f64 lambda1 lambda1 (*.f64 lambda2 (+.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	14.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi2)) (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	4.4b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	52.3b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	8.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	3.6b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
▶	3.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)) (-.f64 phi1 phi2)))
	43.8b	(.f64 R (sqrt.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda2 lambda2) (+.f64 (.f64 phi1 phi1) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (*.f64 lambda2 lambda1))))))
	27.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	29.7b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)

Compiler

Compiled 59908 to 41160 computations (31.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
✓	0.3b	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.1s (6%)

Counts

3 → 72

Calls

3 calls:

383.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)
382.0ms	(exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
379.0ms	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

rewrite112.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`prod-diff_binary64`
471×	`fma-udef_binary64`
283×	`fma-def_binary64`
231×	`fma-neg_binary64`
184×	`log1p-udef_binary64`

Counts

3 → 98

Calls

3 calls:

110.0ms	(exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
110.0ms	(log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
110.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	218	32
2	2593	32
3	4699	32
4	4727	32
5	4935	32

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
660×	`associate-/l*_binary64`
404×	`fma-def_binary64`
348×	`cancel-sign-sub-inv_binary64`
134×	`associate-/r/_binary64`

Counts

170 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1633
1	394	1613
2	1430	1478
3	5231	1478

prune339.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	179	17	196

Error

3.1b

Counts

196 → 17

Alt Table

Status	Error	Program
	27.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	3.6b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	4.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cbrt.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)) (pow.f64 (cbrt.f64 (+.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 1)) 2) -1)) (-.f64 phi1 phi2)))
	4.4b	(.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
▶	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)) (-.f64 phi1 phi2)))
	23.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	37.3b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (fma.f64 lambda1 lambda1 (*.f64 lambda2 (+.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 3)) 1)) (-.f64 phi1 phi2)))
	29.7b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	8.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	43.8b	(.f64 R (sqrt.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda2 lambda2) (+.f64 (.f64 phi1 phi1) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (*.f64 lambda2 lambda1))))))
	7.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2)))) 1)) (-.f64 phi1 phi2)))
	27.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	4.4b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	52.3b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)

Compiler

Compiled 6596 to 4181 computations (36.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))
✓	0.5b	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)
✓	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series737.0ms (3.9%)

Counts

3 → 96

Calls

3 calls:

366.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)
349.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
22.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))

rewrite63.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

923×	`prod-diff_binary64`
143×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
135×	`add-log-exp_binary64`

Counts

3 → 67

Calls

3 calls:

62.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3))
62.0ms	(pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 3)
62.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	292	35
2	3577	35
3	5257	35

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

777×	`cancel-sign-sub-inv_binary64`
601×	`fma-neg_binary64`
301×	`neg-sub0_binary64`
300×	`neg-mul-1_binary64`
260×	`distribute-rgt-neg-in_binary64`

Counts

163 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	2252
1	623	2236
2	2233	2094
3	4299	2088
4	4994	2088

prune277.0ms (1.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	155	17	172

Error

3.1b

Counts

172 → 17

Alt Table

Status	Error	Program
	27.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	3.6b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	7.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2)))) 1)) (-.f64 phi1 phi2)))
	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) 3)) (-.f64 phi1 phi2)))
	27.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 3) 3)) (-.f64 phi1 phi2)))
	23.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	37.3b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (fma.f64 lambda1 lambda1 (*.f64 lambda2 (+.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 3)) 1)) (-.f64 phi1 phi2)))
	29.7b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	8.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	4.4b	(.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	43.8b	(.f64 R (sqrt.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda2 lambda2) (+.f64 (.f64 phi1 phi1) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (*.f64 lambda2 lambda1))))))
▶	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	4.4b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	52.3b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)

Compiler

Compiled 5731 to 3582 computations (37.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)
	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	0.5b	(fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1)
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (7.5%)

Counts

2 → 48

Calls

2 calls:

714.0ms

(fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1)

706.0ms

(-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)

rewrite117.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

643×	`prod-diff_binary64`
444×	`fma-udef_binary64`
339×	`fma-def_binary64`
246×	`fma-neg_binary64`
196×	`expm1-udef_binary64`

Counts

2 → 89

Calls

2 calls:

115.0ms

(-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)

115.0ms

(fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	59
1	262	21
2	2810	21
3	4762	21
4	4779	21
5	4943	21

simplify123.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

570×	`cancel-sign-sub-inv_binary64`
563×	`associate-l_binary64`
449×	`fma-neg_binary64`
440×	`associate-r_binary64`
437×	`distribute-rgt-neg-in_binary64`

Counts

137 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	812
1	161	804
2	458	778
3	1308	736
4	3458	728
5	4545	728
6	4995	728
7	4999	728
8	4959	728

prune548.0ms (2.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	266	19	285

Error

3.1b

Counts

285 → 19

Alt Table

Status	Error	Program
	27.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 1) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (sin.f64 1)))) (-.f64 phi1 phi2)))
	3.6b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	7.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 phi1))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	7.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 1/2 phi2)))) 1)) (-.f64 phi1 phi2)))
	3.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) 3)) (-.f64 phi1 phi2)))
	18.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 1/3) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	37.3b	(.f64 R (hypot.f64 (/.f64 (.f64 (-.f64 (pow.f64 lambda1 3) (pow.f64 lambda2 3)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (fma.f64 lambda1 lambda1 (*.f64 lambda2 (+.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	23.2b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	4.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) 3)) 1)) (-.f64 phi1 phi2)))
	29.7b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	8.2b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	4.4b	(.f64 R (pow.f64 (cbrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (exp.f64 (+.f64 (fma.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi2) 2)) phi1) -1/2 (log1p.f64 (cos.f64 (.f64 1/2 phi2)))) (.f64 (.f64 (/.f64 (.f64 phi1 phi1) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (+.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (+.f64 (cos.f64 (.f64 1/2 phi2)) 1)) (cos.f64 (.f64 1/2 phi2)))) -1/8))) 1)) (-.f64 phi1 phi2)))
	43.8b	(.f64 R (sqrt.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda2 lambda2) (+.f64 (.f64 phi1 phi1) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (*.f64 lambda2 lambda1))))))
	27.9b	(-.f64 (.f64 R phi2) (.f64 phi1 R))
	7.0b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 phi2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	7.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (fma.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 phi2))) 2) 1) 1)) (-.f64 phi1 phi2)))
	4.4b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	52.3b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)

Compiler

Compiled 10450 to 6688 computations (36% saved)

regimes2.4s (12.5%)

Accuracy

Total 0.3b remaining (7.6%)

Threshold costs 0.3b (7.6%)

Counts

189 → 1

Compiler

Compiled 71640 to 50384 computations (29.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	26	28
2	33	28
3	37	28
4	39	28
5	38	28

end367.0ms (1.9%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 716 to 521 computations (27.2% saved)

Details

analyze2.8s (14.8%)

sample5.2s (27.3%)

simplify115.0ms (0.6%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series1.4s (7.2%)

rewrite70.0ms (0.4%)

simplify405.0ms (2.1%)

prune1.2s (6.5%)

localize15.0ms (0.1%)

series1.1s (6%)

rewrite112.0ms (0.6%)

simplify53.0ms (0.3%)

prune339.0ms (1.8%)

localize13.0ms (0.1%)

series737.0ms (3.9%)

rewrite63.0ms (0.3%)

simplify83.0ms (0.4%)

prune277.0ms (1.5%)

localize17.0ms (0.1%)

series1.4s (7.5%)

rewrite117.0ms (0.6%)

simplify123.0ms (0.6%)

prune548.0ms (2.9%)

regimes2.4s (12.5%)

simplify3.0ms (0%)

end367.0ms (1.9%)

Profiling