Details

analyze142.0ms (3.6%)

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 (31.9%)

Results

1.2s	8256×	body	128	valid
2.0ms	16×	body	128	invalid

Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify15.0ms (0.4%)

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

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.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))))
▶	0.3b	(/.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

0.4b

(/.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))))

▶

0.3b

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

series225.0ms (5.7%)

Counts

4 → 84

Calls

4 calls:

119.0ms	(/.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)))
76.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))
25.0ms	(.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))
4.0ms	(sqrt.f64 (fma.f64 (*.f64 v v) -6 2))

rewrite47.0ms (1.2%)

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	90
1	387	90

Stop Event

1×	node limit

Counts

4 → 123

Calls

4 calls:

44.0ms	(/.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)))
44.0ms	(sqrt.f64 (fma.f64 (*.f64 v v) -6 2))
44.0ms	(.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))
44.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 t (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

345×	`associate-/r*_binary64`
291×	`fma-def_binary64`
209×	`associate-r_binary64`
207×	`+-commutative_binary64`
202×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	350	4291
1	1352	4192

Stop Event

1×	node limit

Counts

207 → 221

prune235.0ms (5.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Error

Counts

223 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (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)))
	0.7b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (.f64 t (sqrt.f64 2)))) (-.f64 1 (.f64 v v)))
	0.7b	(/.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (PI.f64) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (.f64 6 (pow.f64 v 2)))))) (-.f64 1 (*.f64 v v)))
	1.0b	(/.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t)) (-.f64 1 (.f64 v v)))
	0.4b	(/.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 9193 to 6168 computations (32.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series236.0ms (5.9%)

Counts

4 → 84

Calls

4 calls:

113.0ms	(/.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)))
96.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))
14.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) t)
12.0ms	(/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))

rewrite64.0ms (1.6%)

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	91
1	419	91

Stop Event

1×	node limit

Counts

4 → 131

Calls

4 calls:

61.0ms	(/.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)))
61.0ms	(/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
61.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) t)
61.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	357	4222
1	1315	4150
2	4811	4150

Stop Event

1×	node limit

Counts

215 → 211

prune223.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	213	4	217

Error

Counts

217 → 4

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (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)))
▶	0.1b	(/.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)))
	1.0b	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 (sqrt.f64 1/2) (PI.f64))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 8790 to 5949 computations (32.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 (*.f64 v v) -6 2))
✓	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)

series203.0ms (5.1%)

Counts

3 → 60

Calls

3 calls:

112.0ms

(/.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)))

77.0ms

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

14.0ms

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

rewrite45.0ms (1.1%)

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

Calls

3 calls:

42.0ms

(/.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)))

42.0ms

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

42.0ms

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

simplify80.0ms (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 (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	238	4	242

Error

Counts

242 → 4

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (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)))
✓	0.1b	(/.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)))
	1.0b	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 (sqrt.f64 1/2) (PI.f64))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 10026 to 6797 computations (32.2% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 t (PI.f64)))
✓	0.3b	(*.f64 t (PI.f64))
✓	0.4b	(.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
✓	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))

series95.0ms (2.4%)

Counts

4 → 60

Calls

4 calls:

76.0ms	(.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
10.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
6.0ms	(/.f64 1 (*.f64 t (PI.f64)))
2.0ms	(*.f64 t (PI.f64))

rewrite76.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
167×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	354	60
2	4389	60

Stop Event

1×	node limit

Counts

4 → 142

Calls

4 calls:

73.0ms	(/.f64 1 (*.f64 t (PI.f64)))
73.0ms	(*.f64 t (PI.f64))
73.0ms	(.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
73.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
494×	`cancel-sign-sub-inv_binary64`
211×	`sub-neg_binary64`
196×	`distribute-neg-in_binary64`
193×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	2189
1	769	2171
2	2816	2097

Stop Event

1×	node limit

Counts

202 → 191

prune163.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (.f64 (/.f64 1 (.f64 t (PI.f64))) (/.f64 (fma.f64 v (.f64 v -5) 1) (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)))
✓	0.1b	(/.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)))
	1.0b	(/.f64 (.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) t) (/.f64 (sqrt.f64 1/2) (PI.f64))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 6936 to 4484 computations (35.4% saved)

regimes242.0ms (6.1%)

Accuracy

Total 0.1b remaining (93%)

Threshold costs 0.1b (93%)

Counts

41 → 1

Compiler

Compiled 5590 to 4049 computations (27.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	26	36
2	33	36
3	37	36
4	39	36

Stop Event

1×

saturated

end93.0ms (2.3%)

Compiler: Compiled 155 to 110 computations (29% saved)

Details

analyze142.0ms (3.6%)

sample1.3s (31.9%)

simplify15.0ms (0.4%)

prune4.0ms (0.1%)

localize13.0ms (0.3%)

series225.0ms (5.7%)

rewrite47.0ms (1.2%)

simplify84.0ms (2.1%)

prune235.0ms (5.9%)

localize15.0ms (0.4%)

series236.0ms (5.9%)

rewrite64.0ms (1.6%)

simplify84.0ms (2.1%)

prune223.0ms (5.6%)

localize13.0ms (0.3%)

series203.0ms (5.1%)

rewrite45.0ms (1.1%)

simplify80.0ms (2%)

prune243.0ms (6.1%)

localize14.0ms (0.4%)

series95.0ms (2.4%)

rewrite76.0ms (1.9%)

simplify50.0ms (1.3%)

prune163.0ms (4.1%)

regimes242.0ms (6.1%)

simplify2.0ms (0.1%)

end93.0ms (2.3%)

Profiling