Details

analyze3.9s (19.9%)

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)

sample142.0ms (0.7%)

Algorithm

1×

intervals

Results

28.0ms	187×	body	128	valid
19.0ms	24×	body	1024	invalid
15.0ms	37×	body	512	valid
15.0ms	21×	body	1024	valid
10.0ms	71×	body	128	invalid
9.0ms	17×	body	512	invalid
3.0ms	11×	body	256	valid
3.0ms	10×	body	256	invalid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1409×	`unsub-neg_binary64`
864×	`distribute-neg-out_binary64`
607×	`neg-sub0_binary64`
531×	`neg-mul-1_binary64`
472×	`distribute-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	49
1	33	49
2	76	49
3	204	49
4	568	49
5	1423	49
6	3464	49
7	3534	49
8	3951	49
9	4094	49
10	4149	49
11	4184	49
12	4960	49

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

39.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	39.6b	(.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

▶

39.6b

(*.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 74 to 42 computations (43.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.1b	(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))))

rewrite332.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

39.6b

Rules

142×	`associate-*l/_binary64`
102×	`flip--_binary64`
102×	`flip3--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`

Counts

4 → 135

Calls

4 calls:

42.0ms	(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))))
10.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8749 to 2698 computations (69.2% saved)

series550.0ms (2.8%)

Error

3.3b

Counts

4 → 75

Calls

4 calls:

342.0ms	(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))))
98.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
14.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
14.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 11824 to 8300 computations (29.8% saved)

simplify212.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

671×	`distribute-rgt-in_binary64`
662×	`distribute-lft-in_binary64`
269×	`*-commutative_binary64`
186×	`associate-r_binary64`
137×	`+-commutative_binary64`

Counts

210 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	694	14574
1	1828	13988
2	5628	13988

prune138.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	185	9	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	9	195

Error

5.0b

Counts

195 → 9

Alt Table

Status	Error	Program
	41.8b	(.f64 R (sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1))) (.f64 2 (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 lambda2 (.f64 (.f64 phi2 lambda1) (sin.f64 (.f64 phi1 1/2))))))) (+.f64 (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (.f64 lambda2 lambda1))) (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 (.f64 phi2 (sin.f64 (.f64 phi1 1/2))) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	42.0b	(.f64 R (+.f64 (-.f64 (+.f64 phi2 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi1)) phi1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi1) (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2)) phi1)))))
	54.4b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	42.2b	(.f64 R (-.f64 (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2))) phi2) (+.f64 phi1 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi2))))
	39.7b	(.f64 R (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	40.1b	(.f64 R (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	47.0b	(*.f64 R (neg.f64 phi1))
	39.9b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
▶	39.6b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 7222 to 3240 computations (55.1% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.2b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
36.1b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite162.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

128×	`associate-*l/_binary64`
96×	`flip--_binary64`
96×	`flip3--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`

Counts

4 → 116

Calls

4 calls:

17.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)

Compiler

Compiled 8400 to 2825 computations (66.4% saved)

series444.0ms (2.3%)

Error

5.0b

Counts

4 → 57

Calls

4 calls:

332.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
29.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)
16.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 10127 to 7153 computations (29.4% saved)

simplify187.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

663×	`distribute-rgt-in_binary64`
654×	`distribute-lft-in_binary64`
260×	`*-commutative_binary64`
166×	`associate-r_binary64`
127×	`associate-l_binary64`

Counts

173 → 148

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	674	12979
1	1718	12233
2	5510	12233

prune101.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	148	9	157

Error

5.0b

Counts

157 → 9

Alt Table

Status	Error	Program
	41.8b	(.f64 R (sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1))) (.f64 2 (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 lambda2 (.f64 (.f64 phi2 lambda1) (sin.f64 (.f64 phi1 1/2))))))) (+.f64 (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (.f64 lambda2 lambda1))) (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 (.f64 phi2 (sin.f64 (.f64 phi1 1/2))) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	42.0b	(.f64 R (+.f64 (-.f64 (+.f64 phi2 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi1)) phi1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi1) (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2)) phi1)))))
	39.9b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	40.1b	(.f64 R (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	54.4b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	42.2b	(.f64 R (-.f64 (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2))) phi2) (+.f64 phi1 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi2))))
	47.0b	(*.f64 R (neg.f64 phi1))
▶	39.7b	(.f64 R (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
✓	39.6b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 6277 to 2776 computations (55.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.2b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
36.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
36.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite262.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

192×	`flip--_binary64`
192×	`associate-*r/_binary64`
192×	`flip3--_binary64`
132×	`sqrt-div_binary64`
128×	`frac-add_binary64`

Counts

4 → 172

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
3.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 17935 to 5315 computations (70.4% saved)

series799.0ms (4.1%)

Error

5.0b

Counts

4 → 76

Calls

4 calls:

336.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
334.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
12.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 20663 to 13818 computations (33.1% saved)

simplify312.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

698×	`distribute-rgt-in_binary64`
689×	`distribute-lft-in_binary64`
245×	`*-commutative_binary64`
159×	`associate-r_binary64`
119×	`+-commutative_binary64`

Counts

248 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	621	22800
1	1561	22002
2	5396	22002

prune177.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	214	9	223

Error

5.0b

Counts

223 → 9

Alt Table

Status	Error	Program
▶	39.9b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	40.1b	(.f64 R (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	54.4b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	42.2b	(.f64 R (-.f64 (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2))) phi2) (+.f64 phi1 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi2))))
	55.7b	(.f64 R (.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 phi2 (/.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)) phi1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)) phi1) (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)) phi1))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	41.8b	(.f64 R (sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1))) (.f64 2 (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 lambda2 (.f64 (.f64 phi2 lambda1) (sin.f64 (.f64 phi1 1/2))))))) (+.f64 (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (.f64 lambda2 lambda1))) (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 (.f64 phi2 (sin.f64 (.f64 phi1 1/2))) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	47.0b	(*.f64 R (neg.f64 phi1))
✓	39.7b	(.f64 R (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
✓	39.6b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 13337 to 5344 computations (59.9% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
0.2b	(.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1))
3.2b	(cos.f64 (*.f64 1/2 (+.f64 phi2 phi1)))

rewrite82.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

21×	`distribute-lft-in_binary64`
21×	`distribute-rgt-in_binary64`
18×	`cancel-sign-sub-inv_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms	(.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1))
7.0ms	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
2.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi2 phi1)))

Compiler

Compiled 1572 to 757 computations (51.8% saved)

series163.0ms (0.8%)

Error

4.8b

Counts

3 → 63

Calls

3 calls:

65.0ms	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
46.0ms	(.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1))
13.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi2 phi1)))

Compiler

Compiled 3693 to 2581 computations (30.1% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-r_binary64`
432×	`distribute-rgt-in_binary64`
384×	`associate-l_binary64`
276×	`sub-neg_binary64`
263×	`*-commutative_binary64`

Counts

138 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	3973
1	830	3781
2	2922	3506
3	5145	3506

prune78.0ms (0.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	6	6
Picked	1	0	1
Done	1	1	2
Total	112	17	129

Error

3.6b

Counts

129 → 17

Alt Table

Status	Error	Program
	54.4b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	40.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)) R)) (cbrt.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)) R))) (cbrt.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)) R)))
	53.6b	(exp.f64 (log.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)) R)))
	44.7b	(-.f64 (+.f64 (.f64 1/2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) (.f64 lambda1 R)))) (+.f64 (.f64 R (.f64 (cos.f64 (.f64 1/2 phi2)) (+.f64 lambda2 (.f64 (.f64 1/8 (.f64 phi1 phi1)) lambda1)))) (.f64 1/48 (.f64 (pow.f64 phi1 3) (.f64 (sin.f64 (.f64 1/2 phi2)) (.f64 lambda2 R)))))) (+.f64 (+.f64 (.f64 1/2 (.f64 lambda2 (.f64 phi1 (.f64 (sin.f64 (.f64 1/2 phi2)) R)))) (.f64 (.f64 (cos.f64 (.f64 1/2 phi2)) R) (+.f64 lambda1 (.f64 1/8 (.f64 (.f64 phi1 phi1) lambda2))))) (.f64 1/48 (.f64 (pow.f64 phi1 3) (.f64 (sin.f64 (.f64 1/2 phi2)) (.f64 lambda1 R))))))
	40.1b	(.f64 R (.f64 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) (sqrt.f64 (-.f64 lambda2 lambda1))) (sqrt.f64 (-.f64 lambda2 lambda1))))
	42.1b	(.f64 (cos.f64 (.f64 1/2 phi2)) (*.f64 (-.f64 lambda2 lambda1) R))
	55.7b	(.f64 R (.f64 (sqrt.f64 (+.f64 (-.f64 (+.f64 phi2 (/.f64 (.f64 lambda2 (.f64 lambda1 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2))) phi1)) phi1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (.f64 lambda1 lambda1) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)) phi1) (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2)) phi1))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	40.8b	(.f64 (cos.f64 (.f64 1/2 phi1)) (*.f64 (-.f64 lambda2 lambda1) R))
	40.3b	(.f64 R (.f64 (.f64 (sqrt.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2)))) (sqrt.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))))) (-.f64 lambda2 lambda1)))
	40.1b	(.f64 R (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 2) (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))))
	38.6b	(.f64 R (.f64 (-.f64 (.f64 (cos.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (sin.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2)))) (-.f64 lambda2 lambda1)))
	42.2b	(.f64 R (-.f64 (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2))) phi2) (+.f64 phi1 (/.f64 (.f64 lambda2 (.f64 (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) 2) lambda1)) phi2))))
	41.8b	(.f64 R (sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1))) (.f64 2 (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 lambda2 (.f64 (.f64 phi2 lambda1) (sin.f64 (.f64 phi1 1/2))))))) (+.f64 (.f64 2 (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (.f64 lambda2 lambda1))) (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 (.f64 phi2 (sin.f64 (.f64 phi1 1/2))) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	47.0b	(*.f64 R (neg.f64 phi1))
	40.3b	(.f64 R (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1))) (cbrt.f64 (.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)))) (cbrt.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)))))
	42.2b	(.f64 R (exp.f64 (log.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) (-.f64 lambda2 lambda1)))))
	39.6b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 2292 to 1338 computations (41.6% saved)

regimes7.0s (35.3%)

Accuracy

Total 16.0b remaining (79.7%)

Threshold costs 0b (0%)

Compiler

Compiled 84002 to 54405 computations (35.2% saved)

bsearch292.0ms (1.5%)

Compiler: Compiled 37 to 21 computations (43.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	158
1	55	158
2	65	158
3	71	158
4	74	158
5	73	158

end41.0ms (0.2%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 756 to 364 computations (51.9% saved)

sample4.0s (20.5%)

Algorithm

1×

intervals

Results

815.0ms	6025×	body	128	valid
620.0ms	807×	body	1024	valid
358.0ms	776×	body	512	valid
346.0ms	473×	body	1024	invalid
318.0ms	2342×	body	128	invalid
177.0ms	406×	body	512	invalid
115.0ms	384×	body	256	valid
52.0ms	181×	body	256	invalid
11.0ms	8×	body	2048	valid

Compiler

Compiled 856 to 526 computations (38.6% saved)

Details

analyze3.9s (19.9%)

sample142.0ms (0.7%)

simplify120.0ms (0.6%)

prune2.0ms (0%)

localize24.0ms (0.1%)

rewrite332.0ms (1.7%)

series550.0ms (2.8%)

simplify212.0ms (1.1%)

prune138.0ms (0.7%)

localize23.0ms (0.1%)

rewrite162.0ms (0.8%)

series444.0ms (2.3%)

simplify187.0ms (0.9%)

prune101.0ms (0.5%)

localize23.0ms (0.1%)

rewrite262.0ms (1.3%)

series799.0ms (4.1%)

simplify312.0ms (1.6%)

prune177.0ms (0.9%)

localize9.0ms (0%)

rewrite82.0ms (0.4%)

series163.0ms (0.8%)

simplify101.0ms (0.5%)

prune78.0ms (0.4%)

regimes7.0s (35.3%)

bsearch292.0ms (1.5%)

simplify7.0ms (0%)

end41.0ms (0.2%)

sample4.0s (20.5%)

Profiling