Details

analyze4.7s (28.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 37 to 28 computations (24.3% saved)

sample2.1s (12.9%)

Results

2.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 51 to 39 computations (23.5% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary32`
7×	`+-commutative_binary32`
6×	`fma-def_binary32`
4×	`*-commutative_binary32`
4×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

prune2.0ms (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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
✓	0.1b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.3b	(*.f32 314159265359/50000000000 u2)

series46.0ms (0.3%)

Counts

4 → 40

Calls

4 calls:

32.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
11.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary32`
69×	`*-un-lft-identity_binary32`
56×	`times-frac_binary32`
50×	`sqrt-prod_binary32`
39×	`add-cube-cbrt_binary32`

Counts

4 → 148

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
6.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)

simplify130.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-/r*_binary32`
481×	`fma-def_binary32`
401×	`times-frac_binary32`
261×	`associate-/l*_binary32`
204×	`fma-neg_binary32`

Counts

188 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	3681
1	635	3497
2	1868	3373
3	4856	3373
4	4924	3373

prune434.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	214	12	226
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	215	12	227

Error

0.1b

Counts

227 → 12

Alt Table

Status	Error	Program
	2.1b	(.f32 (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	6.7b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
	2.4b	(-.f32 (+.f32 (.f32 9740909103402808085817682884085781839780052161/150000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 98696044010906577398881/5000000000000000000000 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.6b	(.f32 (sqrt.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 u1 (cbrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.6b	(.f32 (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))

Compiler

Compiled 5345 to 3929 computations (26.5% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
	0.1b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
✓	0.2b	(.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

series49.0ms (0.3%)

Counts

2 → 32

Calls

2 calls:

34.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

14.0ms

(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary32`
28×	`associate-l_binary32`
26×	`sqrt-prod_binary32`
23×	`*-un-lft-identity_binary32`
19×	`times-frac_binary32`

Counts

2 → 71

Calls

2 calls:

14.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))

8.0ms

(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

402×	`fma-neg_binary32`
320×	`*-commutative_binary32`
299×	`associate-/r*_binary32`
291×	`distribute-neg-frac_binary32`
286×	`fma-def_binary32`

Counts

103 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2028
1	434	1904
2	1285	1784
3	3454	1784
4	4941	1784

prune448.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	230	8	238
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	238	12	250

Error

0.0b

Counts

250 → 12

Alt Table

Status	Error	Program
	6.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
	2.4b	(-.f32 (+.f32 (.f32 9740909103402808085817682884085781839780052161/150000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 98696044010906577398881/5000000000000000000000 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	2.1b	(.f32 (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	6.7b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 1 u1) -1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	1.7b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))

Compiler

Compiled 6990 to 5547 computations (20.6% saved)

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
✓	0.2b	(.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) u2))
✓	0.2b	(.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

series72.0ms (0.4%)

Counts

3 → 44

Calls

3 calls:

42.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))

16.0ms

(*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

14.0ms

(*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`associate-l_binary32`
35×	`add-sqr-sqrt_binary32`
28×	`*-un-lft-identity_binary32`
26×	`sqrt-prod_binary32`
19×	`times-frac_binary32`

Counts

3 → 96

Calls

3 calls:

12.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))

7.0ms

(*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))

5.0ms

(*.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

402×	`fma-neg_binary32`
378×	`*-commutative_binary32`
302×	`unswap-sqr_binary32`
299×	`associate-/r*_binary32`
291×	`distribute-neg-frac_binary32`

Counts

140 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	3208
1	475	2924
2	1397	2179
3	3572	2171
4	5114	2171

prune397.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	235	10	245

Error

0.0b

Counts

245 → 10

Alt Table

Status	Error	Program
	6.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
	1.7b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	2.4b	(-.f32 (+.f32 (.f32 9740909103402808085817682884085781839780052161/150000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 98696044010906577398881/5000000000000000000000 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	2.1b	(.f32 (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2))))
▶	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))

Compiler

Compiled 6479 to 5183 computations (20% saved)

localize65.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1)))))
✓	0.2b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.3b	(.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 u1 u1) (.f32 1 u1))))
	0.3b	(*.f32 314159265359/50000000000 u2)

series85.0ms (0.5%)

Counts

3 → 40

Calls

3 calls:

71.0ms

(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))

10.0ms

(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1)))))

3.0ms

(*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1))))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary32`
46×	`associate-l_binary32`
41×	`*-un-lft-identity_binary32`
37×	`times-frac_binary32`
24×	`difference-of-squares_binary32`

Counts

3 → 114

Calls

3 calls:

21.0ms

(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))

21.0ms

(*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1))))

13.0ms

(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (pow.f32 u1 3))) (+.f32 (*.f32 1 1) (+.f32 (*.f32 u1 u1) (*.f32 1 u1)))))

simplify167.0ms (1%)

Algorithm

1×	egg-herbie

Rules

772×	`times-frac_binary32`
249×	`distribute-rgt-in_binary32`
237×	`distribute-lft-in_binary32`
232×	`associate-l_binary32`
207×	`cancel-sign-sub-inv_binary32`

Counts

154 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	4633
1	874	4297
2	3184	4289
3	4673	4241
4	4918	4241
5	4941	4241

prune496.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	248	9	257

Error

0.0b

Counts

257 → 9

Alt Table

Status	Error	Program
	6.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2))))))
	1.7b	(.f32 (.f32 (sqrt.f32 (/.f32 (+.f32 (fma.f32 u1 u1 u1) (pow.f32 u1 3)) (-.f32 1 (pow.f32 u1 3)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))
	2.4b	(-.f32 (+.f32 (.f32 9740909103402808085817682884085781839780052161/150000000000000000000000000000000000000000000 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 98696044010906577398881/5000000000000000000000 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	2.1b	(.f32 (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2))))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (.f32 (cbrt.f32 314159265359/50000000000) u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (cbrt.f32 314159265359/50000000000) (.f32 (cbrt.f32 314159265359/50000000000) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))))

Compiler

Compiled 9001 to 6433 computations (28.5% saved)

regimes6.3s (39%)

Accuracy

Total 0.3b remaining (75.5%)

Threshold costs 0.3b (75.5%)

Counts

500 → 1

Compiler

Compiled 115147 to 91103 computations (20.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
3×	`*-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	24	35
2	28	35
3	30	35
4	31	35
5	30	35

end227.0ms (1.4%)

Compiler: Compiled 359 to 292 computations (18.7% saved)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Details

analyze4.7s (28.9%)

sample2.1s (12.9%)

simplify18.0ms (0.1%)

prune2.0ms (0%)

localize31.0ms (0.2%)

series46.0ms (0.3%)

rewrite33.0ms (0.2%)

simplify130.0ms (0.8%)

prune434.0ms (2.7%)

localize43.0ms (0.3%)

series49.0ms (0.3%)

rewrite28.0ms (0.2%)

simplify88.0ms (0.5%)

prune448.0ms (2.8%)

localize44.0ms (0.3%)

series72.0ms (0.4%)

rewrite33.0ms (0.2%)

simplify105.0ms (0.7%)

prune397.0ms (2.5%)

localize65.0ms (0.4%)

series85.0ms (0.5%)

rewrite69.0ms (0.4%)

simplify167.0ms (1%)

prune496.0ms (3.1%)

regimes6.3s (39%)

simplify3.0ms (0%)

end227.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17