Details

analyze2.9s (17.5%)

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)

sample109.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	197×	body	128	valid
17.0ms	36×	body	1024	valid
8.0ms	17×	body	1024	invalid
7.0ms	73×	body	128	invalid
5.0ms	14×	body	512	valid
5.0ms	14×	body	512	invalid
2.0ms	9×	body	256	valid
1.0ms	6×	body	256	invalid

Compiler

Compiled 80 to 48 computations (40% saved)

simplify132.0ms (0.8%)

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

prune3.0ms (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

41.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	41.9b	(.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

▶

41.9b

(*.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)

localize16.0ms (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))))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.6b	(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))))

rewrite379.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

41.9b

Rules

142×	`associate-*l/_binary64`
102×	`flip3--_binary64` `flip--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`

Counts

4 → 135

Calls

4 calls:

24.0ms	(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))))
13.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8749 to 2698 computations (69.2% saved)

series1.6s (9.4%)

Error

3.6b

Counts

4 → 69

Calls

4 calls:

1.3s	(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))))
124.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16792 to 12364 computations (26.4% saved)

simplify248.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

671×	`distribute-rgt-in_binary64`
662×	`distribute-lft-in_binary64`
326×	`*-commutative_binary64`
217×	`associate-r_binary64`
157×	`associate-l_binary64`

Counts

204 → 169

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	745	16134
1	2048	14942
2	5840	14942

prune168.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

5.8b

Counts

170 → 8

Alt Table

Status	Error	Program
	48.0b	(.f64 R (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (.f64 lambda2 lambda1) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2))))))
	50.5b	(.f64 R (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1)))
	55.3b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	41.2b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	41.9b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	46.2b	(*.f64 R (neg.f64 phi1))
	42.3b	(.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)))))))
▶	41.1b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda1)) phi2))))

Compiler

Compiled 7164 to 3254 computations (54.6% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.2b	(-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda1)) phi2)))
7.3b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda1 lambda1)) phi2)
7.3b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda1)) phi2))))
7.4b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda2)) phi2)

rewrite310.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

48×	`add-exp-log_binary64`
29×	`*-un-lft-identity_binary64`
24×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
16×	`add-log-exp_binary64`

Counts

4 → 120

Calls

4 calls:

15.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda1)) phi2))))
14.0ms	(-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda1)) phi2)))
10.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda2)) phi2)
10.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda1 lambda1)) phi2)

Compiler

Compiled 9643 to 5271 computations (45.3% saved)

series1.4s (8.1%)

Error

3.6b

Counts

4 → 92

Calls

4 calls:

659.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda1)) phi2))))
438.0ms	(-.f64 (+.f64 phi2 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda2)) phi2) (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda1 lambda1)) phi2)))) (+.f64 phi1 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (.f64 lambda2 lambda1)) phi2)))
95.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda2 lambda2)) phi2)
70.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi2 phi1))) 2) (*.f64 lambda1 lambda1)) phi2)

Compiler

Compiled 12556 to 8783 computations (30% saved)

simplify314.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

344×	`associate-/l*_binary64`
288×	`*-commutative_binary64`
220×	`distribute-rgt-in_binary64`
208×	`distribute-lft-in_binary64`
174×	`associate-r_binary64`

Counts

212 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	696	15798
1	2094	14965
2	4895	14965
3	5005	14965

prune223.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	192	9	201

Error

3.9b

Counts

201 → 9

Alt Table

Status	Error	Program
	48.0b	(.f64 R (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (.f64 lambda2 lambda1) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2))))))
	50.5b	(.f64 R (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1)))
	55.3b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	37.5b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
	41.2b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	41.9b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
▶	36.1b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
	46.2b	(*.f64 R (neg.f64 phi1))
	42.3b	(.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)))))))

Compiler

Compiled 10036 to 5654 computations (43.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
2.9b	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))
5.0b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
7.3b	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2)

rewrite126.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

28×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2)
10.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
3.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
3.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

Compiler

Compiled 2654 to 1514 computations (43% saved)

series366.0ms (2.2%)

Error

3.6b

Counts

4 → 52

Calls

4 calls:

201.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
78.0ms	(/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2)
29.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
17.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

Compiler

Compiled 3912 to 2843 computations (27.3% saved)

simplify182.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

469×	`cancel-sign-sub-inv_binary64`
388×	`distribute-rgt-in_binary64`
370×	`associate-r_binary64`
288×	`associate-l_binary64`
215×	`unswap-sqr_binary64`

Counts

138 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	4184
1	798	3835
2	2741	3702
3	4878	3694
4	4990	3694
5	4976	3694

prune96.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	110	10	120

Error

3.8b

Counts

120 → 10

Alt Table

Status	Error	Program
	48.0b	(.f64 R (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (.f64 lambda2 lambda1) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2))))))
	50.5b	(.f64 R (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1)))
	55.3b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
▶	37.5b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
	53.9b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (exp.f64 (-.f64 (.f64 2 (log.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1))) (log.f64 phi2))))) phi1))
	41.2b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	41.9b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
✓	36.1b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
	46.2b	(*.f64 R (neg.f64 phi1))
	42.3b	(.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)))))))

Compiler

Compiled 2798 to 1675 computations (40.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
2.9b	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))
4.7b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
7.4b	(/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2)

rewrite135.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.8b

Rules

28×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2)
9.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
3.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
3.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

Compiler

Compiled 2654 to 1514 computations (43% saved)

series371.0ms (2.2%)

Error

3.8b

Counts

4 → 52

Calls

4 calls:

203.0ms	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
86.0ms	(/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2)
30.0ms	(pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)
14.0ms	(cos.f64 (*.f64 1/2 (+.f64 phi1 phi2)))

Compiler

Compiled 3941 to 2866 computations (27.3% saved)

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

455×	`cancel-sign-sub-inv_binary64`
393×	`distribute-rgt-in_binary64`
349×	`associate-r_binary64`
290×	`associate-l_binary64`
206×	`unswap-sqr_binary64`

Counts

138 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	319	4215
1	797	3866
2	2829	3754
3	4920	3746
4	4966	3746

prune90.0ms (0.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	113	10	123

Error

3.8b

Counts

123 → 10

Alt Table

Status	Error	Program
	48.0b	(.f64 R (sqrt.f64 (-.f64 (+.f64 (.f64 phi2 phi2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (+.f64 (.f64 lambda2 lambda2) (.f64 lambda1 lambda1)))) (.f64 2 (.f64 (.f64 lambda2 lambda1) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2))))))
	50.5b	(.f64 R (neg.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1)))
	55.3b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda1 lambda2)))
	37.5b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (*.f64 1/2 (+.f64 phi1 phi2))) 2)) phi2))) phi1))
	53.9b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (exp.f64 (-.f64 (.f64 2 (log.f64 (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) lambda1))) (log.f64 phi2))))) phi1))
	41.2b	(.f64 R (.f64 (cos.f64 (*.f64 1/2 (+.f64 phi2 phi1))) (-.f64 lambda2 lambda1)))
	41.9b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) 3)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
	36.1b	(.f64 R (-.f64 (+.f64 phi2 (.f64 1/2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 (+.f64 phi1 phi2))) 2) (*.f64 lambda1 lambda1)) phi2))) phi1))
	46.2b	(*.f64 R (neg.f64 phi1))
	42.3b	(.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)))))))

Compiler

Compiled 2581 to 1527 computations (40.8% saved)

regimes3.6s (21.5%)

Accuracy

Total 20.6b remaining (83.5%)

Threshold costs 0b (0%)

Compiler

Compiled 42692 to 28279 computations (33.8% saved)

bsearch272.0ms (1.6%)

Steps

Iters	Range		Point
10	1.0284686419738535e-51	1.2539551760800909e-39	1.3774337930017817e-42
9	1.2882934747169585e-128	9.388050073423723e-124	2.287702190753648e-124
1	1.7189095683010906e-203	1.8340718707240185e-203	1.7477001439068225e-203
5	-6.255416248066921e-148	-2.4922331348940428e-148	-2.5266019225073433e-148
5	-7.262206615199176e-118	-2.738928216716404e-118	-7.172364672971488e-118
10	-2.91245066075347e+15	-27479.60762666662	-106049510029.62999

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
6×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	184
1	77	184
2	97	184
3	109	184
4	116	184
5	117	184
6	117	184

end41.0ms (0.2%)

Compiler: Compiled 635 to 345 computations (45.7% saved)

sample3.5s (20.8%)

Algorithm

1×

intervals

Results

655.0ms	6046×	body	128	valid
403.0ms	792×	body	1024	valid
265.0ms	742×	body	512	valid
240.0ms	2298×	body	128	invalid
238.0ms	473×	body	1024	invalid
120.0ms	360×	body	512	invalid
99.0ms	418×	body	256	valid
50.0ms	167×	body	256	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 486 to 302 computations (37.9% saved)

Details

analyze2.9s (17.5%)

sample109.0ms (0.6%)

simplify132.0ms (0.8%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite379.0ms (2.3%)

series1.6s (9.4%)

simplify248.0ms (1.5%)

prune168.0ms (1%)

localize30.0ms (0.2%)

rewrite310.0ms (1.8%)

series1.4s (8.1%)

simplify314.0ms (1.9%)

prune223.0ms (1.3%)

localize16.0ms (0.1%)

rewrite126.0ms (0.8%)

series366.0ms (2.2%)

simplify182.0ms (1.1%)

prune96.0ms (0.6%)

localize15.0ms (0.1%)

rewrite135.0ms (0.8%)

series371.0ms (2.2%)

simplify148.0ms (0.9%)

prune90.0ms (0.5%)

regimes3.6s (21.5%)

bsearch272.0ms (1.6%)

simplify10.0ms (0.1%)

end41.0ms (0.2%)

sample3.5s (20.8%)

Profiling