Details

analyze2.8s (21.1%)

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
1.9%	97.2%	0.8%	13
3.5%	95.2%	1.3%	14

Compiler

Compiled 38 to 22 computations (42.1% saved)

sample4.1s (31.1%)

Results

1.4s	6242×	body	128	valid
719.0ms	773×	body	1024	valid
532.0ms	2465×	body	128	invalid
487.0ms	814×	body	512	valid
441.0ms	447×	body	1024	invalid
212.0ms	377×	body	512	invalid
188.0ms	421×	body	256	valid
71.0ms	174×	body	256	invalid
21.0ms	6×	body	2048	valid

Compiler

Compiled 76 to 44 computations (42.1% saved)

preprocess37.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

1000×	`distribute-rgt-in_binary64`
877×	`fma-def_binary64`
324×	`distribute-lft-in_binary64`
228×	`distribute-lft-neg-out_binary64`
228×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	264
1	261	264
2	662	264
3	2716	264
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1013×	`unsub-neg_binary64`
719×	`distribute-neg-out_binary64`
703×	`fma-def_binary64`
272×	`distribute-rgt-in_binary64`
229×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	35	24
2	83	24
3	312	24
4	1070	24
5	3549	24

Stop Event

1×	node limit

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

3.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.7b	(.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)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))
✓	2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series820.0ms (6.3%)

Counts

3 → 132

Calls

33 calls:

314.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	phi2	0
301.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	phi1	0
31.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	R	-inf
29.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	lambda2	0
25.0ms	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (-.f64 phi1 phi2)))	R	0

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`log1p-udef_binary64`
171×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	331	48
2	4470	48

Stop Event

1×	node limit

Counts

3 → 54

simplify258.0ms (2%)

Algorithm

1×	egg-herbie

Rules

849×	`*-commutative_binary64`
666×	`associate-r_binary64`
277×	`+-commutative_binary64`
255×	`fma-def_binary64`
218×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1316	24088
1	4846	24088

Stop Event

1×	node limit

Counts

186 → 184

prune643.0ms (4.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	171	13	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	13	185

Error

3.5b

Counts

185 → 13

Alt Table

Status	Error	Program
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	35.5b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	33.2b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	50.5b	(.f64 (.f64 lambda2 R) (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))
	19.2b	(.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) lambda1) (-.f64 phi1 phi2)))
	3.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))) 3)) (-.f64 phi1 phi2)))
	16.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
	8.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	4.8b	(pow.f64 (cbrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 3)
	52.5b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	31.2b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	50.2b	(.f64 R (hypot.f64 (pow.f64 (pow.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) 3) 1/3) (-.f64 phi1 phi2)))
▶	3.7b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 31974 to 21604 computations (32.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))))
✓	0.4b	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))
✓	2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series404.0ms (3.1%)

Counts

4 → 120

Calls

30 calls:

98.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi2	inf
97.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi2	-inf
85.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi1	inf
85.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi1	-inf
4.0ms	(log1p.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)))	phi2	0

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

970×	`prod-diff_binary64`
131×	`add-sqr-sqrt_binary64`
128×	`expm1-log1p-u_binary64`
127×	`log1p-expm1-u_binary64`
124×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	259	44
2	3417	44

Stop Event

1×	node limit

Counts

4 → 79

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

936×	`times-frac_binary64`
620×	`cancel-sign-sub-inv_binary64`
249×	`fma-neg_binary64`
217×	`sub-neg_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2689
1	610	2669
2	2324	2609

Stop Event

1×	node limit

Counts

199 → 116

prune225.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	114	15	129

Error

3.4b

Counts

129 → 15

Alt Table

Status	Error	Program
	16.5b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 1/2 (.f64 (sin.f64 (.f64 1/2 phi1)) phi2)))) (-.f64 phi1 phi2)))
▶	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi1))) (-.f64 phi1 phi2)))
	35.5b	(exp.f64 (log.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))))
	33.2b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	50.5b	(.f64 (.f64 lambda2 R) (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))
	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (pow.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) 3) 1) (+.f64 (.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1)) (+.f64 1 (.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) 1))))))) (-.f64 phi1 phi2)))
	52.5b	(pow.f64 (pow.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2))) 3) 1/3)
	16.9b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (+.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi1))) (.f64 (.f64 (tan.f64 (/.f64 (.f64 1/2 phi1) 2)) phi2) -1/2)))) (-.f64 phi1 phi2)))
	50.2b	(.f64 R (hypot.f64 (pow.f64 (pow.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) 3) 1/3) (-.f64 phi1 phi2)))
	14.6b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (-.f64 (log1p.f64 (cos.f64 (.f64 1/2 phi2))) (.f64 1/2 (/.f64 phi1 (/.f64 (+.f64 (cos.f64 (.f64 1/2 phi2)) 1) (sin.f64 (.f64 1/2 phi2)))))))) (-.f64 phi1 phi2)))
	19.2b	(.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) lambda1) (-.f64 phi1 phi2)))
	8.4b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (*.f64 1/2 phi2))) (-.f64 phi1 phi2)))
	31.2b	(.f64 R (hypot.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)))) (-.f64 phi1 phi2)))
	10.3b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log.f64 (+.f64 (cos.f64 (*.f64 1/2 phi1)) 1)))) (-.f64 phi1 phi2)))

Compiler

Compiled 4612 to 2909 computations (36.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))
✓	0.3b	(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))
✓	0.3b	(pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)
	2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series368.0ms (2.8%)

Counts

3 → 72

Calls

18 calls:

89.0ms	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))	phi1	inf
88.0ms	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))	phi2	inf
84.0ms	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))	phi2	-inf
84.0ms	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))	phi1	-inf
4.0ms	(log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2)))	phi2	0

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`prod-diff_binary64`
206×	`fma-def_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`
158×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	233	32
2	2547	32

Stop Event

1×	node limit

Counts

3 → 73

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

944×	`times-frac_binary64`
603×	`fma-def_binary64`
377×	`cancel-sign-sub-inv_binary64`
167×	`fma-neg_binary64`
142×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1759
1	470	1738
2	1793	1675

Stop Event

1×	node limit

Counts

145 → 123

prune270.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	12	2	14
Picked	0	1	1
Done	0	0	0
Total	170	5	175

Error

0.1b

Counts

175 → 5

Alt Table

Status	Error	Program
	33.2b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	50.5b	(.f64 (.f64 lambda2 R) (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))))
✓	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (/.f64 (-.f64 (pow.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) 3) 1) (fma.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) (+.f64 1 (.f64 (+.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 1) 1))))) (-.f64 phi1 phi2)))
▶	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 5447 to 3421 computations (37.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (*.f64 phi2 1/2)))
✓	0.1b	(-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))
✓	0.1b	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))))
✓	0.2b	(.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))

series103.0ms (0.8%)

Counts

4 → 120

Calls

30 calls:

9.0ms	(-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))	phi2	-inf
7.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))))	phi1	-inf
6.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))))	lambda1	inf
6.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))))	lambda1	-inf
5.0ms	(.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (*.f64 phi2 1/2)))))	lambda2	inf

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

193×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
181×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	94
1	376	52

Stop Event

1×	node limit

Counts

4 → 124

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

867×	`cancel-sign-sub-inv_binary64`
392×	`fma-neg_binary64`
332×	`associate--r+_binary64`
329×	`associate--l+_binary64`
228×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	4262
1	570	4214
2	2059	3769

Stop Event

1×	node limit

Counts

244 → 195

prune383.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	192	8	200

Error

0.0b

Counts

200 → 8

Alt Table

Status	Error	Program
✓	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 2))))) (-.f64 phi1 phi2)))
	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (fma.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 1/2 phi2)) (.f64 (sin.f64 (.f64 1/2 phi2)) (neg.f64 (sin.f64 (*.f64 phi1 1/2)))))) (-.f64 phi1 phi2)))
	3.7b	(.f64 R (hypot.f64 (/.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 (-.f64 phi1 phi2))) (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))) (-.f64 lambda1 lambda2)) (cos.f64 (.f64 1/2 (-.f64 phi1 phi2)))) (-.f64 phi1 phi2)))
	3.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (/.f64 (-.f64 (pow.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) 3) 1) (fma.f64 (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) (+.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 1) (+.f64 1 (.f64 (+.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) 1) 1))))) (-.f64 phi1 phi2)))
	0.1b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 phi2 1/2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 1/2 phi2))))) 1))) (-.f64 phi1 phi2)))
	33.2b	(pow.f64 (sqrt.f64 (.f64 R (hypot.f64 (.f64 (cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2)) (-.f64 lambda1 lambda2)) (-.f64 phi1 phi2)))) 2)
	0.1b	(.f64 R (hypot.f64 (+.f64 (.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 1/2 phi2))) (-.f64 lambda1 lambda2)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (neg.f64 (sin.f64 (*.f64 phi1 1/2)))) (-.f64 lambda1 lambda2))) (-.f64 phi1 phi2)))
	24.8b	(.f64 R (hypot.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 (pow.f64 (sqrt.f64 (.f64 (cos.f64 (.f64 phi1 1/2)) (cos.f64 (.f64 1/2 phi2)))) 2) (.f64 (sin.f64 (.f64 phi1 1/2)) (sin.f64 (.f64 phi2 1/2))))) (-.f64 phi1 phi2)))

Compiler

Compiled 7681 to 4902 computations (36.2% saved)

regimes2.0s (15.7%)

Accuracy

Total 0.1b remaining (44.9%)

Threshold costs 0.1b (44.9%)

Counts

193 → 1

Compiler

Compiled 48627 to 34823 computations (28.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	36	45
2	50	45
3	60	45
4	65	45
5	66	45

Stop Event

1×

saturated

end191.0ms (1.5%)

Stop Event

1×

fuel

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 494 to 358 computations (27.5% saved)

Details

analyze2.8s (21.1%)

sample4.1s (31.1%)

preprocess37.0ms (0.3%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series820.0ms (6.3%)

rewrite58.0ms (0.4%)

simplify258.0ms (2%)

prune643.0ms (4.9%)

localize14.0ms (0.1%)

series404.0ms (3.1%)

rewrite60.0ms (0.5%)

simplify60.0ms (0.5%)

prune225.0ms (1.7%)

localize20.0ms (0.1%)

series368.0ms (2.8%)

rewrite45.0ms (0.3%)

simplify46.0ms (0.4%)

prune270.0ms (2.1%)

localize20.0ms (0.2%)

series103.0ms (0.8%)

rewrite51.0ms (0.4%)

simplify75.0ms (0.6%)

prune383.0ms (2.9%)

regimes2.0s (15.7%)

simplify3.0ms (0%)

end191.0ms (1.5%)

Profiling