Details

analyze152.0ms (3.3%)

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)

sample1.2s (26.6%)

Results

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

Compiler

Compiled 62 to 44 computations (29% saved)

preprocess27.0ms (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)

simplify15.0ms (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

prune5.0ms (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
▶	0.5b	(/.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)))
	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))))

Status

Error

Program

▶

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)))

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))))

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)))))

series200.0ms (4.3%)

Counts

4 → 84

Calls

21 calls:

30.0ms	(/.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
28.0ms	(/.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
17.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))	t	0

rewrite46.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
176×	`add-cbrt-cube_binary64`
175×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
1	387	88

Stop Event

1×	node limit

Counts

4 → 122

simplify88.0ms (1.9%)

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

206 → 203

prune221.0ms (4.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	199	6	205

Error

0.0b

Counts

205 → 6

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))))
	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))))))
	0.5b	(/.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)))
▶	0.3b	(/.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)))

Compiler

Compiled 8561 to 5643 computations (34.1% saved)

localize14.0ms (0.3%)

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)))))

series220.0ms (4.8%)

Counts

3 → 60

Calls

15 calls:

60.0ms	(/.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
31.0ms	(/.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
28.0ms	(/.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
19.0ms	(.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
18.0ms	(.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

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
193×	`log1p-expm1-u_binary64`
193×	`expm1-log1p-u_binary64`
191×	`add-cbrt-cube_binary64`
190×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	80
1	419	80

Stop Event

1×	node limit

Counts

3 → 102

simplify85.0ms (1.8%)

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

prune267.0ms (5.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	204	4	208

Error

0.0b

Counts

208 → 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)))
	0.5b	(/.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 (.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)))

Compiler

Compiled 8544 to 5773 computations (32.4% 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 (/.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)

series224.0ms (4.9%)

Counts

3 → 60

Calls

15 calls:

34.0ms	(/.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
33.0ms	(/.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
32.0ms	(/.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
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)))	v	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

rewrite58.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`
179×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	87
1	393	87

Stop Event

1×	node limit

Counts

3 → 120

simplify85.0ms (1.8%)

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

prune353.0ms (7.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	220	4	224

Error

0.0b

Counts

224 → 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)))
	0.5b	(/.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 (.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)))

Compiler

Compiled 9388 to 6316 computations (32.7% saved)

localize14.0ms (0.3%)

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))))))

series134.0ms (2.9%)

Counts

3 → 60

Calls

15 calls:

32.0ms	(.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
29.0ms	(.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
29.0ms	(.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
8.0ms	(.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
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	0

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

199×	`add-sqr-sqrt_binary64`
189×	`log1p-expm1-u_binary64`
189×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
186×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	70
1	413	70

Stop Event

1×	node limit

Counts

3 → 129

simplify67.0ms (1.4%)

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

prune262.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	212	4	216

Error

0.0b

Counts

216 → 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)))
	0.5b	(/.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 (.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)))

Compiler

Compiled 7738 to 5206 computations (32.7% saved)

regimes625.0ms (13.6%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

87 → 1

Compiler

Compiled 12659 to 9126 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

end102.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 162 to 114 computations (29.6% saved)

Details

analyze152.0ms (3.3%)

sample1.2s (26.6%)

preprocess27.0ms (0.6%)

simplify15.0ms (0.3%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series200.0ms (4.3%)

rewrite46.0ms (1%)

simplify88.0ms (1.9%)

prune221.0ms (4.8%)

localize14.0ms (0.3%)

series220.0ms (4.8%)

rewrite45.0ms (1%)

simplify85.0ms (1.8%)

prune267.0ms (5.8%)

localize13.0ms (0.3%)

series224.0ms (4.9%)

rewrite58.0ms (1.3%)

simplify85.0ms (1.8%)

prune353.0ms (7.7%)

localize14.0ms (0.3%)

series134.0ms (2.9%)

rewrite45.0ms (1%)

simplify67.0ms (1.4%)

prune262.0ms (5.7%)

regimes625.0ms (13.6%)

simplify3.0ms (0.1%)

end102.0ms (2.2%)

Profiling