Details

analyze147.0ms (3.4%)

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)

sample1.2s (27.4%)

Results

1.2s	8256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 62 to 44 computations (29% saved)

preprocess28.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

710×	`associate-/l*_binary64`
254×	`fma-def_binary64`
248×	`distribute-neg-frac_binary64`
237×	`associate-/l/_binary64`
232×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	86
1	102	86
2	363	76
3	1860	72
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 30 to 21 computations (30% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
467×	`associate-/r*_binary64`
351×	`associate-/l*_binary64`
245×	`associate-l_binary64`
222×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	190	38
3	949	36

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.6b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
▶	0.5b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))

Status

Error

Program

0.6b

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

▶

0.5b

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

Compiler

Compiled 166 to 113 computations (31.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series211.0ms (4.9%)

Counts

4 → 84

Calls

21 calls:

33.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	-inf
29.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	0
27.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	inf
20.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))	t	-inf
19.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))	t	0

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary64`
183×	`*-un-lft-identity_binary64`
183×	`pow1_binary64`
178×	`add-cbrt-cube_binary64`
178×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
1	386	88

Stop Event

1×	node limit

Counts

4 → 119

simplify89.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

325×	`fma-neg_binary64`
323×	`associate-/r*_binary64`
275×	`fma-def_binary64`
204×	`associate-r_binary64`
198×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	325	4077
1	1263	3996
2	4771	3996

Stop Event

1×	node limit

Counts

203 → 200

prune218.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	196	6	202

Error

0.0b

Counts

202 → 6

Alt Table

Status	Error	Program
	32.3b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) -6 2)) t)))) 2) (-.f64 1 (*.f64 v v)))
	0.8b	(.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 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))
	0.6b	(/.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 (/.f64 1 (.f64 t (PI.f64))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (-.f64 1 (*.f64 v v)))
	0.5b	(/.f64 (/.f64 (log.f64 (exp.f64 (fma.f64 v (.f64 v -5) 1))) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))
	0.6b	(/.f64 (neg.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (neg.f64 (.f64 t (PI.f64))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 8479 to 5590 computations (34.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series187.0ms (4.3%)

Counts

3 → 60

Calls

15 calls:

30.0ms	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	-inf
27.0ms	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	inf
27.0ms	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))	t	0
20.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))	t	-inf
17.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))	t	inf

rewrite44.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
198×	`*-un-lft-identity_binary64`
198×	`pow1_binary64`
193×	`add-cbrt-cube_binary64`
193×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	80
1	418	80

Stop Event

1×	node limit

Counts

3 → 102

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

352×	`associate-/r*_binary64`
304×	`fma-def_binary64`
239×	`fma-neg_binary64`
230×	`associate-+r+_binary64`
216×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	348	3925
1	1291	3853
2	4764	3853

Stop Event

1×	node limit

Counts

162 → 175

prune201.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

0.0b

Counts

207 → 4

Alt Table

Status	Error	Program
	0.3b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))
▶	0.1b	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))
	0.6b	(/.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 (/.f64 1 (.f64 t (PI.f64))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (-.f64 1 (*.f64 v v)))
	0.5b	(/.f64 (/.f64 (log.f64 (exp.f64 (fma.f64 v (.f64 v -5) 1))) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 8516 to 5748 computations (32.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 v (*.f64 v -5) 1)
✓	0.0b	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))
✓	0.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))
✓	0.1b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) t)

series183.0ms (4.2%)

Counts

3 → 60

Calls

15 calls:

29.0ms	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))	t	-inf
27.0ms	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))	t	0
26.0ms	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))	t	inf
20.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) t)	t	-inf
17.0ms	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) t)	t	0

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

196×	`add-sqr-sqrt_binary64`
187×	`*-un-lft-identity_binary64`
187×	`pow1_binary64`
182×	`add-cbrt-cube_binary64`
182×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	87
1	392	87

Stop Event

1×	node limit

Counts

3 → 120

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-/r*_binary64`
306×	`fma-def_binary64`
255×	`fma-neg_binary64`
243×	`associate-+r+_binary64`
229×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	351	4051
1	1319	3977
2	4833	3977

Stop Event

1×	node limit

Counts

180 → 193

prune243.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	219	4	223

Error

0.0b

Counts

223 → 4

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))
✓	0.1b	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))
	0.6b	(/.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 (/.f64 1 (.f64 t (PI.f64))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (-.f64 1 (*.f64 v v)))
	0.5b	(/.f64 (/.f64 (log.f64 (exp.f64 (fma.f64 v (.f64 v -5) 1))) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 9362 to 6301 computations (32.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series175.0ms (4.1%)

Counts

3 → 60

Calls

15 calls:

48.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))	t	inf
45.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))	t	-inf
30.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))	t	0
13.0ms	(.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))	v	inf
7.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))	v	-inf

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

204×	`add-sqr-sqrt_binary64`
194×	`*-un-lft-identity_binary64`
194×	`pow1_binary64`
189×	`add-cbrt-cube_binary64`
189×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	70
1	412	70

Stop Event

1×	node limit

Counts

3 → 129

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

566×	`cancel-sign-sub-inv_binary64`
298×	`sub-neg_binary64`
251×	`associate-/r*_binary64`
249×	`fma-neg_binary64`
212×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	270	2780
1	970	2675
2	3727	2675

Stop Event

1×	node limit

Counts

189 → 185

prune307.0ms (7.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	211	4	215

Error

0.0b

Counts

215 → 4

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (-.f64 1 (.f64 v v)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))
✓	0.1b	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) t) (-.f64 1 (.f64 v v)))
	0.6b	(/.f64 (.f64 (fma.f64 v (.f64 v -5) 1) (/.f64 (/.f64 1 (.f64 t (PI.f64))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (-.f64 1 (*.f64 v v)))
	0.5b	(/.f64 (/.f64 (log.f64 (exp.f64 (fma.f64 v (.f64 v -5) 1))) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 7710 to 5188 computations (32.7% saved)

regimes511.0ms (11.8%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

85 → 1

Compiler

Compiled 12379 to 8926 computations (27.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	28	36
2	35	36
3	39	36
4	41	36

Stop Event

1×

saturated

end105.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 162 to 114 computations (29.6% saved)

Details

analyze147.0ms (3.4%)

sample1.2s (27.4%)

preprocess28.0ms (0.6%)

simplify14.0ms (0.3%)

prune6.0ms (0.1%)

localize13.0ms (0.3%)

series211.0ms (4.9%)

rewrite49.0ms (1.1%)

simplify89.0ms (2.1%)

prune218.0ms (5%)

localize16.0ms (0.4%)

series187.0ms (4.3%)

rewrite44.0ms (1%)

simplify81.0ms (1.9%)

prune201.0ms (4.7%)

localize14.0ms (0.3%)

series183.0ms (4.2%)

rewrite45.0ms (1%)

simplify88.0ms (2%)

prune243.0ms (5.6%)

localize16.0ms (0.4%)

series175.0ms (4.1%)

rewrite50.0ms (1.1%)

simplify90.0ms (2.1%)

prune307.0ms (7.1%)

regimes511.0ms (11.8%)

simplify3.0ms (0.1%)

end105.0ms (2.4%)

Profiling