Details

analyze374.0ms (3.6%)

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)

sample76.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true
0.0ms	1×	pre	128	false

Compiler

Compiled 54 to 42 computations (22.2% saved)

simplify9.0ms (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)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (*.f32 314159265359/50000000000 u2))
✓	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)

series37.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

31.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(cos.f32 (*.f32 314159265359/50000000000 u2))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary32`
50×	`*-un-lft-identity_binary32`
37×	`times-frac_binary32`
30×	`associate-l_binary32`
29×	`add-cube-cbrt_binary32`

Counts

4 → 119

Calls

4 calls:

11.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
3.0ms	(*.f32 314159265359/50000000000 u2)
1.0ms	(cos.f32 (*.f32 314159265359/50000000000 u2))

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-l_binary32`
431×	`fma-def_binary32`
378×	`associate-/r*_binary32`
357×	`times-frac_binary32`
249×	`associate-/l*_binary32`

Counts

155 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	2854
1	565	2690
2	1637	2568
3	4598	2568
4	4961	2568

prune282.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	186	8	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	8	195

Error

0.1b

Counts

195 → 8

Alt Table

Status	Error	Program
	0.7b	(.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 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.4b	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	3.1b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.4b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (/.f32 (-.f32 1 u1) (sqrt.f32 u1)))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
▶	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.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 314159265359/50000000000 u2))))

Compiler

Compiled 4261 to 3126 computations (26.6% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series65.0ms (0.6%)

Counts

2 → 32

Calls

2 calls:

61.0ms	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 1 u1))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-l_binary32`
24×	`add-sqr-sqrt_binary32`
19×	`*-un-lft-identity_binary32`
16×	`times-frac_binary32`
14×	`add-cube-cbrt_binary32`

Counts

2 → 75

Calls

2 calls:

11.0ms	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
10.0ms	(.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 1 u1))

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

800×	`fma-def_binary32`
568×	`times-frac_binary32`
454×	`distribute-rgt-in_binary32`
191×	`fma-neg_binary32`
169×	`associate-l_binary32`

Counts

107 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2889
1	659	2508
2	2100	2343
3	4766	2343
4	4948	2343

prune275.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	201	8	209

Error

0.1b

Counts

209 → 8

Alt Table

Status	Error	Program
	0.7b	(.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 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.4b	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	3.1b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
▶	0.3b	(.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.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 314159265359/50000000000 u2))))

Compiler

Compiled 5446 to 3628 computations (33.4% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series64.0ms (0.6%)

Counts

2 → 32

Calls

2 calls:

61.0ms	(.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))))
3.0ms	(/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary32`
31×	`times-frac_binary32`
30×	`*-un-lft-identity_binary32`
24×	`associate-r_binary32`
23×	`sqrt-prod_binary32`

Counts

2 → 83

Calls

2 calls:

11.0ms	(.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))))
4.0ms	(/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))

simplify136.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

591×	`times-frac_binary32`
387×	`fma-def_binary32`
320×	`associate-/l*_binary32`
293×	`associate-/r*_binary32`
179×	`fma-neg_binary32`

Counts

115 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	3247
1	493	3023
2	1597	2870
3	4626	2868
4	4977	2868
5	4938	2868

prune273.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	199	8	207

Error

0.1b

Counts

207 → 8

Alt Table

Status	Error	Program
	0.7b	(.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 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
▶	0.4b	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	3.1b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.3b	(.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.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 314159265359/50000000000 u2))))

Compiler

Compiled 5409 to 3108 computations (42.5% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series32.0ms (0.3%)

Counts

3 → 44

Calls

3 calls:

27.0ms	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
3.0ms	(/.f32 1 (/.f32 (-.f32 1 u1) u1))
2.0ms	(/.f32 (-.f32 1 u1) u1)

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

282×	`times-frac_binary32`
223×	`add-sqr-sqrt_binary32`
209×	`*-un-lft-identity_binary32`
132×	`add-cube-cbrt_binary32`
76×	`sqrt-prod_binary32`

Counts

3 → 255

Calls

3 calls:

22.0ms	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
9.0ms	(/.f32 1 (/.f32 (-.f32 1 u1) u1))
5.0ms	(/.f32 (-.f32 1 u1) u1)

simplify192.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-/r*_binary32`
448×	`fma-def_binary32`
401×	`associate-/l*_binary32`
304×	`associate-/r/_binary32`
203×	`fma-neg_binary32`

Counts

299 → 398

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	6074
1	582	5438
2	1896	5204
3	4544	5203
4	5009	5203

prune537.0ms (5.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	420	0	420
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	420	8	428

Error

0.1b

Counts

428 → 8

Alt Table

Status	Error	Program
	0.7b	(.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 (sqrt.f32 (/.f32 1 (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	3.1b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.3b	(.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1)))))
	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 314159265359/50000000000 u2)) (cbrt.f32 (.f32 314159265359/50000000000 u2))) (cbrt.f32 (.f32 314159265359/50000000000 u2)))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.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 314159265359/50000000000 u2))))

Compiler

Compiled 10049 to 7507 computations (25.3% saved)

regimes5.7s (55.3%)

Accuracy

Total 0.2b remaining (66.4%)

Threshold costs 0.2b (66.4%)

Counts

420 → 1

Compiler

Compiled 96754 to 74321 computations (23.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	30	32
2	36	32
3	40	32
4	42	32
5	39	32

end1.0ms (0%)

Compiler: Compiled 24 to 16 computations (33.3% saved)

sample1.7s (16.8%)

Algorithm

1×

intervals

Results

723.0ms	8000×	body	128	valid
291.0ms	8000×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 241 to 185 computations (23.2% 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

analyze374.0ms (3.6%)

sample76.0ms (0.7%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize30.0ms (0.3%)

series37.0ms (0.4%)

rewrite29.0ms (0.3%)

simplify115.0ms (1.1%)

prune282.0ms (2.7%)

localize45.0ms (0.4%)

series65.0ms (0.6%)

rewrite27.0ms (0.3%)

simplify104.0ms (1%)

prune275.0ms (2.7%)

localize41.0ms (0.4%)

series64.0ms (0.6%)

rewrite24.0ms (0.2%)

simplify136.0ms (1.3%)

prune273.0ms (2.7%)

localize36.0ms (0.3%)

series32.0ms (0.3%)

rewrite68.0ms (0.7%)

simplify192.0ms (1.9%)

prune537.0ms (5.2%)

regimes5.7s (55.3%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (16.8%)

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