Details

analyze5.8s (20.9%)

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)

sample6.5s (23.4%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

2.1s	6225×	body	128	valid
1.4s	814×	body	1024	valid
800.0ms	2507×	body	128	invalid
760.0ms	519×	body	1024	invalid
695.0ms	773×	body	512	valid
332.0ms	372×	body	512	invalid
270.0ms	439×	body	256	valid
103.0ms	166×	body	256	invalid
15.0ms	5×	body	2048	valid

Compiler

Compiled 113 to 65 computations (42.5% saved)

simplify114.0ms (0.4%)

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

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

2.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))

Compiler

Compiled 95 to 55 computations (42.1% saved)

localize11.0ms (0%)

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)))
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
✓	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.0s (10.8%)

Counts

4 → 180

Calls

4 calls:

1.8s	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
1.2s	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
21.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

rewrite76.0ms (0.3%)

Algorithm

2×	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 → 73

Calls

4 calls:

74.0ms	(hypot.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2))
74.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))
74.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
74.0ms	(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
0	0	0
1	0	0

simplify459.0ms (1.6%)

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

253 → 269

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2196	44761
1	5035	44761

prune1.2s (4.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	255	14	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	256	14	270

Error

2.3b

Counts

270 → 14

Alt Table

Status	Error	Program
	2.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	26.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (+.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 phi1)) (pow.f64 phi2 3)))) (fma.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2) (.f64 1/8 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2)))))) (-.f64 phi1 phi2)))
	57.6b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	8.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	39.2b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	3.2b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) (-.f64 phi1 phi2)))
	22.5b	(.f64 R (hypot.f64 (-.f64 (fma.f64 1/2 (.f64 lambda2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))) (fma.f64 1/8 (.f64 lambda2 (.f64 (.f64 phi1 phi1) (cos.f64 (.f64 1/2 phi2)))) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1))) (fma.f64 1/2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) lambda1)) (fma.f64 1/8 (.f64 (.f64 phi1 phi1) (.f64 (cos.f64 (.f64 1/2 phi2)) lambda1)) (.f64 lambda2 (cos.f64 (*.f64 1/2 phi2)))))) (-.f64 phi1 phi2)))
	7.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	29.6b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	6.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
▶	2.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))) (-.f64 phi1 phi2)))
	51.0b	(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 60024 to 41248 computations (31.3% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))
✓	0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))
✓	0.6b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series55.0ms (0.2%)

Counts

3 → 96

Calls

3 calls:

27.0ms

(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)

23.0ms

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

5.0ms

(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))

rewrite64.0ms (0.2%)

Algorithm

2×	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 → 65

Calls

3 calls:

63.0ms

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

63.0ms

(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))

63.0ms

(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	291	36
2	3573	36
3	5253	36
0	0	0
1	0	0

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

907×	`cancel-sign-sub-inv_binary64`
476×	`sub-neg_binary64`
377×	`associate--l+_binary64`
354×	`fma-neg_binary64`
249×	`associate-r_binary64`

Counts

161 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2176
1	562	2172
2	2080	2049
3	4391	2049
4	5000	2049
5	4987	2049

prune273.0ms (1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	150	14	164

Error

2.3b

Counts

164 → 14

Alt Table

Status	Error	Program
▶	2.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	2.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	22.5b	(.f64 R (hypot.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda1 (.f64 1/8 (.f64 (.f64 phi1 phi1) lambda2)))) (-.f64 (.f64 (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))) (-.f64 lambda2 lambda1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda2 (.f64 (.f64 (*.f64 phi1 phi1) 1/8) lambda1))))) (-.f64 phi1 phi2)))
	51.0b	(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)
	39.2b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) (-.f64 phi1 phi2)))
	7.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	29.6b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	8.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	57.6b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	6.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	26.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) (-.f64 (.f64 1/48 (pow.f64 phi2 3)) (.f64 1/2 phi2))) (.f64 (.f64 phi2 phi2) (.f64 (cos.f64 (*.f64 1/2 phi1)) -1/8))))) (-.f64 phi1 phi2)))

Compiler

Compiled 5355 to 3253 computations (39.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))
✓	0.4b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
✓	0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series492.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

474.0ms

(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

12.0ms

(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

5.0ms

(*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))

rewrite85.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

628×	`prod-diff_binary64`
202×	`fma-def_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
170×	`log-pow_binary64`

Counts

3 → 69

Calls

3 calls:

83.0ms

(*.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))

83.0ms

(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

83.0ms

(cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	261	32
2	2671	32
3	4845	32
4	4845	32
0	0	0
1	0	0

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`sub-neg_binary64`
246×	`distribute-rgt-neg-in_binary64`
243×	`neg-sub0_binary64`

Counts

141 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1692
1	487	1671
2	1722	1581
3	4500	1581
4	5256	1581

prune364.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	181	14	195

Error

2.2b

Counts

195 → 14

Alt Table

Status	Error	Program
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) 1/3))) (-.f64 phi1 phi2)))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 phi2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2/3))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))) (-.f64 phi1 phi2)))
	26.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) (-.f64 (.f64 1/48 (pow.f64 phi2 3)) (.f64 1/2 phi2))) (.f64 (.f64 phi2 phi2) (.f64 (cos.f64 (*.f64 1/2 phi1)) -1/8))))) (-.f64 phi1 phi2)))
	39.2b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
▶	3.2b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	7.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	29.6b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	8.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	57.6b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	6.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	22.5b	(.f64 R (hypot.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda1 (.f64 1/8 (.f64 (.f64 phi1 phi1) lambda2)))) (-.f64 (.f64 (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))) (-.f64 lambda2 lambda1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda2 (.f64 (.f64 (*.f64 phi1 phi1) 1/8) lambda1))))) (-.f64 phi1 phi2)))

Compiler

Compiled 7660 to 4832 computations (36.9% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
✓	0.2b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2)
	3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.8s (17.4%)

Counts

3 → 124

Calls

3 calls:

3.1s

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

1.7s

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

22.0ms

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

rewrite76.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

319×	`expm1-udef_binary64`
319×	`log1p-udef_binary64`
177×	`add-sqr-sqrt_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`

Counts

3 → 55

Calls

3 calls:

75.0ms

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

75.0ms

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

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	355	60
2	4425	60
3	5302	60
0	0	0
1	0	0

simplify362.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1132×	`associate-r_binary64`
431×	`fma-def_binary64`
380×	`associate-+r+_binary64`
147×	`associate-l_binary64`
60×	`sub-neg_binary64`

Counts

179 → 193

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2067	42836
1	5615	42836

prune1.1s (3.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	223	15	238

Error

2.2b

Counts

238 → 15

Alt Table

Status	Error	Program
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (sqrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)) (-.f64 phi1 phi2)))
	8.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) 1/3))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (pow.f64 (sqrt.f64 (hypot.f64 (.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 2))
	7.9b	(.f64 R (expm1.f64 (log1p.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	6.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 phi2))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (hypot.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2))) 3) (-.f64 phi1 phi2)))
	23.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2/3))) (pow.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2) 1/3))) (-.f64 phi1 phi2)))
	26.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (+.f64 (cos.f64 (.f64 1/2 phi1)) (+.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) (-.f64 (.f64 1/48 (pow.f64 phi2 3)) (.f64 1/2 phi2))) (.f64 (.f64 phi2 phi2) (.f64 (cos.f64 (*.f64 1/2 phi1)) -1/8))))) (-.f64 phi1 phi2)))
	3.2b	(.f64 R (.f64 (pow.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)) 1/4) (.f64 (pow.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)) 1/4) (sqrt.f64 (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))))))
	39.2b	(-.f64 (fma.f64 R phi2 (/.f64 (.f64 lambda2 (.f64 R (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)))) phi1)) (fma.f64 1/2 (/.f64 (.f64 R (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (.f64 lambda1 lambda1))) phi1) (fma.f64 phi1 R (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (.f64 R (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)))))
	29.6b	(expm1.f64 (log1p.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	8.2b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 3))) (-.f64 phi1 phi2)))
	57.6b	(-.f64 (.f64 R (.f64 lambda1 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))) (.f64 lambda2 (.f64 R (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))))))
	6.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 3))) (-.f64 phi1 phi2)))
	22.5b	(.f64 R (hypot.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda1 (.f64 1/8 (.f64 (.f64 phi1 phi1) lambda2)))) (-.f64 (.f64 (.f64 1/2 (.f64 phi1 (sin.f64 (.f64 1/2 phi2)))) (-.f64 lambda2 lambda1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda2 (.f64 (.f64 (*.f64 phi1 phi1) 1/8) lambda1))))) (-.f64 phi1 phi2)))

Compiler

Compiled 57916 to 40209 computations (30.6% saved)

regimes2.4s (8.7%)

Accuracy

Total 0.3b remaining (9.4%)

Threshold costs 0.3b (9.4%)

Counts

188 → 1

Compiler

Compiled 59760 to 41888 computations (29.9% 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	17	29
1	24	29
2	32	29
3	36	29
4	38	29
5	38	29

end316.0ms (1.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 658 to 452 computations (31.3% saved)

Details

analyze5.8s (20.9%)

sample6.5s (23.4%)

simplify114.0ms (0.4%)

prune4.0ms (0%)

localize11.0ms (0%)

series3.0s (10.8%)

rewrite76.0ms (0.3%)

simplify459.0ms (1.6%)

prune1.2s (4.3%)

localize13.0ms (0%)

series55.0ms (0.2%)

rewrite64.0ms (0.2%)

simplify102.0ms (0.4%)

prune273.0ms (1%)

localize19.0ms (0.1%)

series492.0ms (1.8%)

rewrite85.0ms (0.3%)

simplify79.0ms (0.3%)

prune364.0ms (1.3%)

localize13.0ms (0%)

series4.8s (17.4%)

rewrite76.0ms (0.3%)

simplify362.0ms (1.3%)

prune1.1s (3.9%)

regimes2.4s (8.7%)

simplify3.0ms (0%)

end316.0ms (1.1%)

Profiling