Details

analyze1.3s (10.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample169.0ms (1.4%)

Algorithm

1×

intervals

Results

33.0ms	66×	body	1024	valid
30.0ms	63×	body	1024	invalid
16.0ms	149×	body	128	valid
15.0ms	31×	body	512	valid
6.0ms	20×	body	512	invalid
3.0ms	25×	body	128	invalid
2.0ms	11×	body	256	invalid
2.0ms	10×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.9b

Counts

2 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
▶	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 89 to 60 computations (32.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite314.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

40×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
24×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`

Counts

4 → 174

Calls

4 calls:

15.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
15.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
14.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 3604 to 1926 computations (46.6% saved)

series89.0ms (0.7%)

Error

0.8b

Counts

4 → 26

Calls

4 calls:

27.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
23.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
11.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
11.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1512 to 1118 computations (26.1% saved)

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

870×	`associate-/l*_binary64`
496×	`unswap-sqr_binary64`
229×	`associate-/r/_binary64`
166×	`associate-/l/_binary64`
156×	`associate-r_binary64`

Counts

200 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2516
1	412	2244
2	1783	2224
3	5695	2224

prune72.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	66	12	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	13	80

Error

0.7b

Counts

80 → 13

Alt Table

Status	Error	Program
	15.9b	(+.f64 (.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	15.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a2 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
▶	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	20.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	15.7b	(+.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a1 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
	1.0b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	17.9b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (sqrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a2 4))))
	1.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	18.5b	(+.f64 (sqrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a1 4))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))

Compiler

Compiled 1968 to 1248 computations (36.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th)))
0.4b	(/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite366.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`add-cube-cbrt_binary64`
34×	`add-exp-log_binary64`
24×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`

Counts

4 → 177

Calls

4 calls:

17.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
16.0ms	(/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
14.0ms	(.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th)))
14.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 3961 to 1918 computations (51.6% saved)

series101.0ms (0.8%)

Error

0.7b

Counts

4 → 29

Calls

4 calls:

26.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
22.0ms	(/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
19.0ms	(.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th)))
10.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1763 to 1314 computations (25.5% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

619×	`unswap-sqr_binary64`
294×	`times-frac_binary64`
212×	`associate-r_binary64`
206×	`associate-l_binary64`
194×	`log-prod_binary64`

Counts

206 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2779
1	544	2483
2	2833	2405
3	5596	2405

prune122.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	95	9	104
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	100	17	117

Error

0.5b

Counts

117 → 17

Alt Table

Status	Error	Program
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (*.f64 a2 a2)))
	15.7b	(+.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a1 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	18.5b	(+.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (pow.f64 a1 4)) (neg.f64 (sqrt.f64 2))) (neg.f64 (sqrt.f64 2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
▶	1.0b	(+.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1)))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	22.3b	(+.f64 (/.f64 (cbrt.f64 (pow.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))) 3)) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	15.9b	(+.f64 (.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	15.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a2 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	20.6b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (*.f64 a2 a2)))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	18.5b	(+.f64 (sqrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a1 4))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))

Compiler

Compiled 2846 to 1683 computations (40.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))
0.2b	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite430.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-exp-log_binary64`
35×	`add-cube-cbrt_binary64`
24×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`

Counts

4 → 182

Calls

4 calls:

19.0ms	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
19.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
16.0ms	(/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))
14.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 5878 to 4014 computations (31.7% saved)

series273.0ms (2.2%)

Error

0.5b

Counts

4 → 25

Calls

4 calls:

144.0ms	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
51.0ms	(/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))
32.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 2101 to 1716 computations (18.3% saved)

simplify137.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

335×	`unswap-sqr_binary64`
239×	`times-frac_binary64`
186×	`associate-/l*_binary64`
184×	`fma-neg_binary64`
174×	`associate-r_binary64`

Counts

207 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	4001
1	598	2946
2	2718	2474
3	4870	2474
4	4928	2474

prune149.0ms (1.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	109	16	125

Error

0.5b

Counts

125 → 16

Alt Table

Status	Error	Program
✓	1.0b	(+.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1)))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	22.3b	(+.f64 (/.f64 (cbrt.f64 (pow.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))) 3)) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.9b	(+.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	15.9b	(+.f64 (.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	15.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a2 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))
	20.6b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (*.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (*.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.2b	(+.f64 (/.f64 (neg.f64 (cos.f64 th)) (/.f64 (neg.f64 (sqrt.f64 2)) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	18.5b	(+.f64 (sqrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a1 4))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))

Compiler

Compiled 3314 to 2159 computations (34.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 (*.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
0.3b	(.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite396.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`add-exp-log_binary64`
35×	`add-cube-cbrt_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-cbrt-cube_binary64`
18×	`pow1_binary64`

Counts

4 → 177

Calls

4 calls:

18.0ms	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 (*.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
16.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
16.0ms	(.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 5496 to 3641 computations (33.8% saved)

series254.0ms (2.1%)

Error

0.5b

Counts

4 → 25

Calls

4 calls:

147.0ms	(/.f64 (.f64 (neg.f64 (cos.f64 th)) (.f64 (/.f64 (*.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
33.0ms	(.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 1/2))
33.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
13.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 2135 to 1750 computations (18% saved)

simplify145.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

462×	`unswap-sqr_binary64`
216×	`associate-r_binary64`
216×	`associate-l_binary64`
173×	`fma-def_binary64`
165×	`log-prod_binary64`

Counts

202 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3775
1	616	3367
2	2800	3317
3	4945	3317
4	4970	3317

prune160.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	5	9	14
Picked	1	0	1
Done	0	1	1
Total	105	13	118

Error

0.5b

Counts

118 → 13

Alt Table

Status	Error	Program
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.2b	(+.f64 (/.f64 1 (/.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (.f64 (.f64 a1 a1) (cbrt.f64 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (neg.f64 (cos.f64 th))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1)))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (cbrt.f64 (neg.f64 (.f64 (cos.f64 th) (.f64 a1 a1))))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	1.1b	(+.f64 (.f64 (/.f64 (neg.f64 (cos.f64 th)) (.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (/.f64 (/.f64 (.f64 (.f64 a1 a1) (cbrt.f64 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	20.6b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (/.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (*.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (*.f64 a2 a2)))
	1.0b	(+.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	18.5b	(+.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (.f64 (pow.f64 (/.f64 (.f64 a1 a1) (pow.f64 (cbrt.f64 -1) 2)) 2) (pow.f64 (cbrt.f64 1/2) 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	15.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 a2 4))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))

Compiler

Compiled 3038 to 2086 computations (31.3% saved)

regimes3.4s (28%)

Accuracy

Total 0.4b remaining (80.2%)

Threshold costs 0.4b (80.2%)

Compiler

Compiled 76856 to 57232 computations (25.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	49
1	36	49
2	47	47
3	63	47
4	74	47
5	85	47
6	91	47
7	94	47
8	95	47
9	95	47

end8.0ms (0.1%)

Compiler: Compiled 96 to 75 computations (21.9% saved)

sample4.0s (32.9%)

Algorithm

1×

intervals

Results

927.0ms	1903×	body	1024	valid
798.0ms	1644×	body	1024	invalid
482.0ms	4735×	body	128	valid
279.0ms	938×	body	512	valid
246.0ms	798×	body	512	invalid
84.0ms	422×	body	256	valid
83.0ms	426×	body	256	invalid
66.0ms	631×	body	128	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 503 to 367 computations (27% saved)

Details

analyze1.3s (10.9%)

sample169.0ms (1.4%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite314.0ms (2.6%)

series89.0ms (0.7%)

simplify86.0ms (0.7%)

prune72.0ms (0.6%)

localize14.0ms (0.1%)

rewrite366.0ms (3%)

series101.0ms (0.8%)

simplify95.0ms (0.8%)

prune122.0ms (1%)

localize19.0ms (0.2%)

rewrite430.0ms (3.5%)

series273.0ms (2.2%)

simplify137.0ms (1.1%)

prune149.0ms (1.2%)

localize22.0ms (0.2%)

rewrite396.0ms (3.2%)

series254.0ms (2.1%)

simplify145.0ms (1.2%)

prune160.0ms (1.3%)

regimes3.4s (28%)

simplify7.0ms (0.1%)

end8.0ms (0.1%)

sample4.0s (32.9%)

Profiling