Details

analyze159.0ms (0.3%)

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)

sample1.3s (2.4%)

Results

1.2s	8256×	body	128	valid
2.0ms	12×	body	128	invalid

Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify33.0ms (0.1%)

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

prune3.0ms (0%)

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)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
✓	0.2b	(*.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)))))
✓	0.4b	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series202.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

143.0ms	(/.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)))))
49.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
8.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
2.0ms	(*.f64 (PI.f64) t)

rewrite31.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 112

Calls

4 calls:

8.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
8.0ms	(/.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)))))
3.0ms	(*.f64 (PI.f64) t)
1.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))

simplify140.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
492×	`associate-l_binary64`
482×	`associate-/r*_binary64`
433×	`times-frac_binary64`
256×	`associate-/l*_binary64`

Counts

172 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	7020
1	1319	6443
2	4898	6428
3	5385	6428

prune335.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	224	7	231
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	224	8	232

Error

0.0b

Counts

232 → 8

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
▶	0.3b	(/.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))))))))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
✓	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)))))
	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))))
	0.5b	(.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)))))
	41.1b	(cbrt.f64 (/.f64 (pow.f64 (fma.f64 v (.f64 v -5) 1) 3) (.f64 (pow.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) 3) (.f64 (pow.f64 (-.f64 1 (.f64 v v)) 3) (.f64 (pow.f64 (PI.f64) 3) (pow.f64 t 3))))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 (.f64 v v) 6)))))

Compiler

Compiled 9953 to 6380 computations (35.9% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 v 2) (PI.f64))
✓	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))))))))

series363.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

273.0ms	(/.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))))))))
77.0ms	(.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)))))
3.0ms	(*.f64 (pow.f64 v 2) (PI.f64))

rewrite51.0ms (0.1%)

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×	`add-cbrt-cube_binary64`

Counts

4 → 121

Calls

4 calls:

15.0ms	(.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 (pow.f64 v 2) (PI.f64))

simplify143.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

503×	`associate-r_binary64`
475×	`associate-l_binary64`
340×	`associate-/r*_binary64`
233×	`fma-def_binary64`
216×	`times-frac_binary64`

Counts

169 → 265

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	439	7357
1	1311	6616
2	4953	6616

prune443.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	262	3	265
Fresh	5	1	6
Picked	1	0	1
Done	1	0	1
Total	269	4	273

Error

Counts

273 → 4

Alt Table

Status	Error	Program
	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 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 v 2) (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)))))) (.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)))))))))
	0.4b	(.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)))))))
▶	0.3b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (sqrt.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))))))

Compiler

Compiled 14151 to 10410 computations (26.4% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

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

series190.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

161.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (sqrt.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))))))
20.0ms	(/.f64 (sqrt.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)))))
7.0ms	(.f64 (PI.f64) (.f64 v v))
2.0ms	(.f64 (.f64 v v) 6)

rewrite58.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-cbrt-cube_binary64`
40×	`add-exp-log_binary64`
36×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
26×	`associate-l_binary64`

Counts

4 → 148

Calls

4 calls:

21.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (sqrt.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))))))
8.0ms	(/.f64 (sqrt.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)))))
4.0ms	(.f64 (.f64 v v) 6)
4.0ms	(.f64 (PI.f64) (.f64 v v))

simplify170.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

459×	`fma-def_binary64`
433×	`associate-/r*_binary64`
381×	`associate-l_binary64`
381×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Counts

208 → 258

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	508	8995
1	1457	8259
2	4842	8139
3	5025	8139

prune404.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	258	4	262

Error

Counts

262 → 4

Alt Table

Status	Error	Program
	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 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 v 2) (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)))))) (.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)))))))))
	0.4b	(.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)))))))
✓	0.3b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (sqrt.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))))))

Compiler

Compiled 13671 to 8492 computations (37.9% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.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 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3))))
✓	0.4b	(.f64 t (-.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3)))
✓	0.4b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 v 2) (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)))))) (.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)))))))))

series1.3s (2.5%)

Counts

3 → 72

Calls

3 calls:

681.0ms

(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))) (+.f64 (*.f64 (*.f64 (*.f64 (pow.f64 v 2) (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)))))) (*.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)))))))))

470.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3))))

188.0ms

(*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3)))

rewrite3.1s (5.8%)

Algorithm

1×	rewrite-expression-head

Rules

6022×	`associate-*r/_binary64`
4692×	`sqrt-div_binary64`
2349×	`flip--_binary64`
2349×	`flip3--_binary64`
2082×	`frac-times_binary64`

Counts

3 → 1314

Calls

3 calls:

113.0ms

(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2)))))) (+.f64 (*.f64 (*.f64 (*.f64 (pow.f64 v 2) (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)))))) (*.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)))))))))

22.0ms

(*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3)))

12.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 t (-.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (*.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (*.f64 6 (pow.f64 v 2))))) 3))))

simplify9.1s (16.9%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
65×	`neg-mul-1_binary64`
61×	`neg-sub0_binary64`
57×	`fma-udef_binary64`
49×	`sub-neg_binary64`

Counts

1386 → 2527

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3914	453007
1	4771	445977
2	4994	445977

prune33.7s (62.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	2771	0	2771
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	2771	4	2775

Error

Counts

2775 → 4

Alt Table

Status	Error	Program
	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 (fma.f64 v (.f64 v -5) 1) (.f64 t (-.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3) (pow.f64 (.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) 3)))) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2))))) (.f64 (PI.f64) (sqrt.f64 (-.f64 2 (.f64 6 (pow.f64 v 2)))))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 v 2) (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)))))) (.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)))))))))
	0.4b	(.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)))))))
✓	0.3b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) t) (/.f64 (sqrt.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))))))

Compiler

Compiled 776827 to 588869 computations (24.2% saved)

regimes2.2s (4.2%)

Accuracy

Total 0.1b remaining (81.4%)

Threshold costs 0.1b (81.4%)

Counts

307 → 1

Compiler

Compiled 79948 to 59564 computations (25.5% saved)

simplify3.0ms (0%)

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	21	53
1	38	53
2	58	53
3	68	53
4	74	53
5	75	53
6	73	53

end143.0ms (0.3%)

Compiler: Compiled 308 to 232 computations (24.7% saved)

Details

analyze159.0ms (0.3%)

sample1.3s (2.4%)

simplify33.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0%)

series202.0ms (0.4%)

rewrite31.0ms (0.1%)

simplify140.0ms (0.3%)

prune335.0ms (0.6%)

localize14.0ms (0%)

series363.0ms (0.7%)

rewrite51.0ms (0.1%)

simplify143.0ms (0.3%)

prune443.0ms (0.8%)

localize16.0ms (0%)

series190.0ms (0.4%)

rewrite58.0ms (0.1%)

simplify170.0ms (0.3%)

prune404.0ms (0.8%)

localize24.0ms (0%)

series1.3s (2.5%)

rewrite3.1s (5.8%)

simplify9.1s (16.9%)

prune33.7s (62.7%)

regimes2.2s (4.2%)

simplify3.0ms (0%)

end143.0ms (0.3%)

Profiling