Details

analyze137.0ms (2.5%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample64.0ms (1.2%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 106 to 73 computations (31.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
✓	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.5b	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series208.0ms (3.7%)

Counts

4 → 72

Calls

4 calls:

144.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
43.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
18.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
2.0ms	(*.f64 (PI.f64) t)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
9.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
6.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
3.0ms	(*.f64 (PI.f64) t)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-r_binary64`
513×	`associate-l_binary64`
460×	`associate-/r*_binary64`
416×	`times-frac_binary64`
245×	`associate-/l*_binary64`

Counts

203 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	7617
1	1247	6841
2	5223	6841

prune251.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	6	226
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	6	227

Error

0.0b

Counts

227 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
▶	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
	32.2b	(.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))))
	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (.f64 t (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))

Compiler

Compiled 9553 to 5927 computations (38% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 6 (pow.f64 v 2))
✓	0.2b	(.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
✓	0.2b	(.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))))
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))

series322.0ms (5.8%)

Counts

4 → 48

Calls

4 calls:

235.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
74.0ms	(.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))))
10.0ms	(.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
2.0ms	(*.f64 6 (pow.f64 v 2))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64`
26×	`sqrt-div_binary64`
26×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`

Counts

4 → 121

Calls

4 calls:

11.0ms	(.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))))
10.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))))
7.0ms	(.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))
4.0ms	(*.f64 6 (pow.f64 v 2))

simplify156.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-r_binary64`
459×	`associate-l_binary64`
340×	`associate-/r*_binary64`
235×	`fma-def_binary64`
204×	`times-frac_binary64`

Counts

169 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	452	7301
1	1325	6576
2	4946	6576
3	5010	6576

prune565.0ms (10.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	306	3	309
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	310	5	315

Error

Counts

315 → 5

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))
	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	0.3b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (-.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))))
	0.6b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (-.f64 2 (.f64 (.f64 v v) 6)) (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (.f64 (PI.f64) (pow.f64 v 4))))))) (+.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))))

Compiler

Compiled 15755 to 11687 computations (25.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (PI.f64) (.f64 v v))
✓	0.2b	(.f64 (.f64 v v) 6)
✓	0.2b	(.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v)))))
✓	0.3b	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))

series286.0ms (5.1%)

Counts

4 → 72

Calls

4 calls:

150.0ms	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))
129.0ms	(.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v)))))
3.0ms	(.f64 (PI.f64) (.f64 v v))
3.0ms	(.f64 (.f64 v v) 6)

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-exp-log_binary64`
44×	`add-cbrt-cube_binary64`
32×	`frac-times_binary64`
30×	`prod-exp_binary64`
25×	`pow1_binary64`

Counts

4 → 173

Calls

4 calls:

13.0ms	(.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v)))))
11.0ms	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))
4.0ms	(.f64 (.f64 v v) 6)
4.0ms	(.f64 (PI.f64) (.f64 v v))

simplify235.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-def_binary64`
432×	`associate-/r*_binary64`
327×	`times-frac_binary64`
290×	`associate-/l*_binary64`
215×	`*-commutative_binary64`

Counts

245 → 302

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	600	11049
1	1722	10111
2	4891	9959
3	5350	9959

prune373.0ms (6.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	302	5	307

Error

Counts

307 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))
	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
▶	0.3b	(/.f64 (/.f64 1 (/.f64 t (fma.f64 v (.f64 v -5) 1))) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))))
	0.6b	(.f64 (/.f64 1 (.f64 t (.f64 (-.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (pow.f64 v 4) (.f64 (PI.f64) (PI.f64)))) (sqrt.f64 (-.f64 4 (.f64 (pow.f64 v 4) 36)))))) (.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) 6))) (+.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))

Compiler

Compiled 14535 to 8491 computations (41.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
	0.2b	(.f64 (PI.f64) (.f64 v v))
	0.2b	(.f64 (.f64 v v) 6)
✓	0.3b	(/.f64 (/.f64 1 (/.f64 t (fma.f64 v (.f64 v -5) 1))) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))))

series146.0ms (2.6%)

Counts

2 → 36

Calls

2 calls:

142.0ms	(/.f64 (/.f64 1 (/.f64 t (fma.f64 v (.f64 v -5) 1))) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))))
4.0ms	(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`times-frac_binary64`
74×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
74×	`add-cube-cbrt_binary64`
47×	`add-exp-log_binary64`

Counts

2 → 150

Calls

2 calls:

16.0ms	(/.f64 (/.f64 1 (/.f64 t (fma.f64 v (.f64 v -5) 1))) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))))
3.0ms	(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))

simplify210.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

354×	`associate-/r*_binary64`
214×	`*-commutative_binary64`
213×	`associate-l_binary64`
204×	`sub-neg_binary64`
202×	`associate-r_binary64`

Counts

186 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	416	9344
1	1119	8210
2	4273	8051
3	4980	8051
4	4963	8051

prune328.0ms (5.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	317	2	319
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	319	5	324

Error

Counts

324 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1 (.f64 (/.f64 t (fma.f64 v (.f64 v -5) 1)) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (*.f64 v v))))))
	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	0.3b	(/.f64 (/.f64 1 (/.f64 t (fma.f64 v (.f64 v -5) 1))) (.f64 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))) (-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))))
	0.7b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) (-.f64 1 (.f64 v v))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (*.f64 v v) 6)))))
	0.3b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))) t) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 13514 to 8092 computations (40.1% saved)

regimes833.0ms (15%)

Accuracy

Total 0.3b remaining (95.6%)

Threshold costs 0.3b (95.6%)

Counts

121 → 1

Compiler

Compiled 22653 to 16332 computations (27.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`distribute-rgt-neg-in_binary64`
5×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	37	42
2	57	42
3	67	42
4	73	42
5	74	42
6	72	42

end1.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

sample1.0s (18.5%)

Algorithm

1×

intervals

Results

692.0ms	8000×	body	128	valid
1.0ms	13×	body	128	nan

Compiler

Compiled 204 to 145 computations (28.9% saved)

Details

analyze137.0ms (2.5%)

sample64.0ms (1.2%)

simplify31.0ms (0.6%)

prune4.0ms (0.1%)

localize16.0ms (0.3%)

series208.0ms (3.7%)

rewrite41.0ms (0.7%)

simplify121.0ms (2.2%)

prune251.0ms (4.5%)

localize14.0ms (0.3%)

series322.0ms (5.8%)

rewrite47.0ms (0.8%)

simplify156.0ms (2.8%)

prune565.0ms (10.2%)

localize14.0ms (0.2%)

series286.0ms (5.1%)

rewrite58.0ms (1%)

simplify235.0ms (4.2%)

prune373.0ms (6.7%)

localize15.0ms (0.3%)

series146.0ms (2.6%)

rewrite50.0ms (0.9%)

simplify210.0ms (3.8%)

prune328.0ms (5.9%)

regimes833.0ms (15%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.0s (18.5%)

Profiling