Details

analyze168.0ms (2.9%)

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%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.4s (23.8%)

Results

1.3s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.5b	(.f64 (.f64 b b) (+.f64 a 3))

series72.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
27.0ms	(pow.f64 (hypot.f64 a b) 4)
9.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite78.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
306×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	371	70
2	4305	70
3	5096	70

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

72.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
72.0ms	(pow.f64 (hypot.f64 a b) 4)
72.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
72.0ms	(.f64 (.f64 b b) (+.f64 a 3))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-l_binary64`
719×	`fma-def_binary64`
624×	`fma-neg_binary64`
505×	`associate-+l+_binary64`
341×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1855
1	207	1761
2	710	1597
3	2967	1573
4	5116	1573

Stop Event

1×	node limit

Counts

197 → 149

prune225.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	10.6b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)))
▶	0.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))) 2)) -1))
	11.1b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
	51.2b	(.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (fma.f64 2 (.f64 b b) (.f64 a -4))))
	11.9b	(fma.f64 a (.f64 a 4) (fma.f64 (.f64 b b) (+.f64 (fma.f64 b b 12) (.f64 a (+.f64 4 (.f64 a 2)))) -1))

Compiler

Compiled 4885 to 2854 computations (41.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))) 2)
	0.5b	(.f64 (.f64 b b) (+.f64 a 3))
✓	9.1b	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))

series225.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

89.0ms

(pow.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) 2)

83.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) 2))

53.0ms

(cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`prod-diff_binary64`
235×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	301	67
2	3292	67
3	4884	67

Stop Event

1×	node limit

Counts

3 → 61

Calls

3 calls:

60.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) 2))

60.0ms

(pow.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) 2)

60.0ms

(cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary64`
411×	`times-frac_binary64`
318×	`associate-/r*_binary64`
298×	`associate-l_binary64`
297×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	460	6192
1	1654	5851
2	5192	5851

Stop Event

1×	node limit

Counts

133 → 169

prune577.0ms (10.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	305	5	310

Error

Counts

310 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	10.6b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)))
	51.2b	(.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (fma.f64 2 (.f64 b b) (.f64 a -4))))
	4.6b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)) -1))
	11.9b	(fma.f64 a (.f64 a 4) (fma.f64 (.f64 b b) (+.f64 (fma.f64 b b 12) (.f64 a (+.f64 4 (.f64 a 2)))) -1))

Compiler

Compiled 22234 to 15144 computations (31.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
	0.5b	(.f64 (.f64 b b) (+.f64 a 3))

series35.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

21.0ms

(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

13.0ms

(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

rewrite71.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`prod-diff_binary64`
201×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
193×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	68
1	429	68
2	4741	68
3	6353	68

Stop Event

1×	node limit

Counts

2 → 55

Calls

2 calls:

68.0ms

(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

68.0ms

(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-l_binary64`
609×	`fma-def_binary64`
558×	`fma-neg_binary64`
528×	`cancel-sign-sub-inv_binary64`
496×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1227
1	180	1183
2	607	1008
3	2680	990
4	4858	990
5	4993	990
6	4963	990

Stop Event

1×	node limit

Counts

103 → 86

prune218.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	153	5	158

Error

Counts

158 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	10.6b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)))
	51.2b	(.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (fma.f64 2 (.f64 b b) (.f64 a -4))))
▶	4.6b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)) -1))
	11.9b	(fma.f64 a (.f64 a 4) (fma.f64 (.f64 b b) (+.f64 (fma.f64 b b 12) (.f64 a (+.f64 4 (.f64 a 2)))) -1))

Compiler

Compiled 6487 to 3538 computations (45.5% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3))
	0.5b	(.f64 (.f64 b b) (+.f64 a 3))
	9.1b	(cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))
✓	30.5b	(pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)

series192.0ms (3.4%)

Counts

2 → 36

Calls

2 calls:

186.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3))

5.0ms

(pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary64`
192×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`
183×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	418	52
2	4678	52
3	5044	52

Stop Event

1×	node limit

Counts

2 → 36

Calls

2 calls:

63.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3))

63.0ms

(pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)

simplify109.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
529×	`associate-/r*_binary64`
458×	`associate-/l*_binary64`
434×	`fma-def_binary64`
156×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	481	7630
1	1712	7439
2	5183	7439

Stop Event

1×	node limit

Counts

72 → 98

prune529.0ms (9.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	200	5	205

Error

Counts

205 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	10.6b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)))
	51.2b	(.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (fma.f64 2 (.f64 b b) (.f64 a -4))))
✓	4.6b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (.f64 (cbrt.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 a 2) (pow.f64 a 3)) 2) 1/3)) -1))
	11.9b	(fma.f64 a (.f64 a 4) (fma.f64 (.f64 b b) (+.f64 (fma.f64 b b 12) (.f64 a (+.f64 4 (.f64 a 2)))) -1))

Compiler

Compiled 19230 to 14031 computations (27% saved)

regimes1.2s (20.8%)

Accuracy

Total 0.0b remaining (47.9%)

Threshold costs 0.0b (47.9%)

Counts

183 → 1

Compiler

Compiled 27641 to 19595 computations (29.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	51
1	35	51
2	38	51
3	40	51
4	41	51
5	40	51

Stop Event

1×

saturated

end142.0ms (2.5%)

Compiler: Compiled 241 to 162 computations (32.8% saved)

Details

analyze168.0ms (2.9%)

sample1.4s (23.8%)

simplify53.0ms (0.9%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

series72.0ms (1.3%)

rewrite78.0ms (1.4%)

simplify80.0ms (1.4%)

prune225.0ms (3.9%)

localize16.0ms (0.3%)

series225.0ms (3.9%)

rewrite64.0ms (1.1%)

simplify98.0ms (1.7%)

prune577.0ms (10.1%)

localize17.0ms (0.3%)

series35.0ms (0.6%)

rewrite71.0ms (1.2%)

simplify93.0ms (1.6%)

prune218.0ms (3.8%)

localize23.0ms (0.4%)

series192.0ms (3.4%)

rewrite64.0ms (1.1%)

simplify109.0ms (1.9%)

prune529.0ms (9.2%)

regimes1.2s (20.8%)

simplify3.0ms (0.1%)

end142.0ms (2.5%)

Profiling