Details

analyze629.0ms (10.2%)

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%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.4s (38.2%)

Results

774.0ms	5353×	body	128	valid
596.0ms	1147×	body	2048	valid
327.0ms	775×	body	1024	valid
282.0ms	414×	body	4096	valid
141.0ms	1057×	body	128	invalid
128.0ms	389×	body	512	valid
39.0ms	178×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1220×	`fma-neg_binary64`
367×	`fma-def_binary64`
351×	`times-frac_binary64`
266×	`associate-/l*_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	69	22
3	160	22
4	264	22
5	433	22
6	744	22
7	1341	22
8	2769	22
9	4702	22

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

32.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
▶	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	2.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series126.0ms (2%)

Counts

4 → 96

Calls

4 calls:

55.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

rewrite71.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
158×	`egg-rr`
150×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	74
1	302	62
2	4451	62

Stop Event

1×	node limit

Counts

4 → 158

Calls

4 calls:

67.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
67.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
488×	`associate-/l*_binary64`
414×	`associate-/r*_binary64`
400×	`fma-def_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2325
1	429	2249
2	1471	2208

Stop Event

1×	node limit

Counts

254 → 233

prune180.0ms (2.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	220	13	233
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	221	14	235

Error

7.2b

Counts

235 → 14

Alt Table

Status	Error	Program
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
▶	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	45.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -3)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))) (.f64 3 a))
	34.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 3)) (*.f64 3 a))
	45.4b	(/.f64 (.f64 (.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	46.7b	(-.f64 (.f64 1/2 (/.f64 c b)) (.f64 2/3 (/.f64 b a)))
	46.4b	(/.f64 -2/3 (/.f64 a b))
	35.8b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))))) (*.f64 3 a))
	41.5b	(*.f64 (/.f64 -1/2 b) c)
	41.4b	(*.f64 -1/2 (/.f64 c b))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	44.7b	(.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 1/3) (/.f64 1 a))
	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (/.f64 1 (.f64 a -3)))

Compiler

Compiled 6326 to 3957 computations (37.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 c (.f64 a -3) (.f64 b b))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
✓	2.2b	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
✓	19.9b	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))

series126.0ms (2%)

Counts

4 → 96

Calls

4 calls:

53.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
35.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
27.0ms	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))
10.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
148×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	300	62
2	4144	62

Stop Event

1×	node limit

Counts

4 → 136

Calls

4 calls:

57.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))
57.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
57.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
57.0ms	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
487×	`associate-/l*_binary64`
414×	`associate-/r*_binary64`
404×	`fma-def_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2325
1	429	2249
2	1471	2208

Stop Event

1×	node limit

Counts

232 → 211

prune123.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	211	14	225

Error

7.2b

Counts

225 → 14

Alt Table

Status	Error	Program
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	45.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -3)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))) (.f64 3 a))
	34.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 3)) (*.f64 3 a))
	45.4b	(/.f64 (.f64 (.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
▶	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	46.4b	(/.f64 -2/3 (/.f64 a b))
	35.8b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))))) (*.f64 3 a))
	41.5b	(*.f64 (/.f64 -1/2 b) c)
	41.4b	(*.f64 -1/2 (/.f64 c b))
	46.4b	(*.f64 (/.f64 b a) -2/3)
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	44.7b	(.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 1/3) (/.f64 1 a))
	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (/.f64 1 (.f64 a -3)))

Compiler

Compiled 5451 to 3275 computations (39.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1/3 a)
✓	1.0b	(fma.f64 b b (.f64 a (.f64 c -3)))
✓	2.2b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)
✓	19.9b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3))))

series73.0ms (1.2%)

Counts

4 → 76

Calls

4 calls:

34.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)
28.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3))))
9.0ms	(fma.f64 b b (.f64 a (.f64 c -3)))
2.0ms	(/.f64 1/3 a)

rewrite62.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`prod-diff_binary64`
230×	`log1p-udef_binary64`
138×	`egg-rr`
129×	`add-sqr-sqrt_binary64`
123×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	260	42
2	3272	42

Stop Event

1×	node limit

Counts

4 → 138

Calls

4 calls:

59.0ms	(/.f64 1/3 a)
59.0ms	(fma.f64 b b (.f64 a (.f64 c -3)))
59.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)
59.0ms	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3))))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
278×	`associate-r_binary64`
278×	`associate-/l*_binary64`
254×	`associate-/r*_binary64`
241×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	1652
1	275	1584
2	884	1558
3	4841	1558

Stop Event

1×	node limit

Counts

214 → 189

prune146.0ms (2.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	187	16	203

Error

7.2b

Counts

203 → 16

Alt Table

Status	Error	Program
	46.4b	(/.f64 -2/3 (/.f64 a b))
	35.3b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b))) (/.f64 1/3 a))
	41.5b	(*.f64 (/.f64 -1/2 b) c)
	33.5b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	36.7b	(.f64 (-.f64 (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3))))) 3) b) (/.f64 1/3 a))
	45.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -3)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))) (.f64 3 a))
	45.4b	(/.f64 (.f64 (.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
▶	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (/.f64 1 (.f64 a -3)))
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (/.f64 1 a)))
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	41.4b	(*.f64 -1/2 (/.f64 c b))
	46.4b	(*.f64 (/.f64 b a) -2/3)
	44.0b	(.f64 (.f64 (*.f64 a (/.f64 c b)) -3/2) (/.f64 1/3 a))
	44.7b	(.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 1/3) (/.f64 1 a))

Compiler

Compiled 4991 to 3146 computations (37% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 a -3))
✓	1.0b	(fma.f64 b b (.f64 c (.f64 a -3)))
✓	2.2b	(-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
✓	19.9b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))

series75.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

37.0ms	(-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
26.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))
9.0ms	(fma.f64 b b (.f64 c (.f64 a -3)))
3.0ms	(/.f64 1 (*.f64 a -3))

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
141×	`egg-rr`
124×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	253	42
2	3196	42

Stop Event

1×	node limit

Counts

4 → 141

Calls

4 calls:

63.0ms	(/.f64 1 (*.f64 a -3))
63.0ms	(fma.f64 b b (.f64 c (.f64 a -3)))
63.0ms	(-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
63.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

455×	`times-frac_binary64`
407×	`fma-neg_binary64`
274×	`associate-/l*_binary64`
268×	`associate-r_binary64`
252×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1684
1	257	1618
2	813	1604
3	4438	1602

Stop Event

1×	node limit

Counts

229 → 195

prune158.0ms (2.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	195	16	211

Error

7.2b

Counts

211 → 16

Alt Table

Status	Error	Program
	46.4b	(/.f64 -2/3 (/.f64 a b))
	35.3b	(.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b))) (/.f64 1/3 a))
	41.5b	(*.f64 (/.f64 -1/2 b) c)
	33.5b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	36.7b	(.f64 (-.f64 (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3))))) 3) b) (/.f64 1/3 a))
	45.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -3)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))) (.f64 3 a))
	45.4b	(/.f64 (.f64 (.f64 (/.f64 a b) c) -3/2) (*.f64 3 a))
✓	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (/.f64 1 (.f64 a -3)))
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (/.f64 1 a)))
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	41.4b	(*.f64 -1/2 (/.f64 c b))
	46.4b	(*.f64 (/.f64 b a) -2/3)
	44.0b	(.f64 (.f64 (*.f64 a (/.f64 c b)) -3/2) (/.f64 1/3 a))
	44.7b	(.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) 1/3) (/.f64 1 a))

Compiler

Compiled 6032 to 4085 computations (32.3% saved)

regimes1.4s (22.3%)

Accuracy

Total 4.4b remaining (42.9%)

Threshold costs 0b (0%)

Counts

105 → 3

Compiler

Compiled 10445 to 7401 computations (29.1% saved)

bsearch86.0ms (1.4%)

Steps

Iters	Range		Point
10	3.73241376909039e-65	6.985216029906585e-55	1.2049630298744359e-60
9	-1.1839448174746177e+114	-1.8526072091911443e+105	-8.139148106210706e+113

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	35	48
2	38	48
3	39	48

Stop Event

1×

saturated

end168.0ms (2.7%)

Compiler: Compiled 318 to 222 computations (30.2% saved)

Details

analyze629.0ms (10.2%)

sample2.4s (38.2%)

simplify32.0ms (0.5%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series126.0ms (2%)

rewrite71.0ms (1.2%)

simplify52.0ms (0.8%)

prune180.0ms (2.9%)

localize10.0ms (0.2%)

series126.0ms (2%)

rewrite60.0ms (1%)

simplify46.0ms (0.8%)

prune123.0ms (2%)

localize10.0ms (0.2%)

series73.0ms (1.2%)

rewrite62.0ms (1%)

simplify58.0ms (0.9%)

prune146.0ms (2.4%)

localize9.0ms (0.1%)

series75.0ms (1.2%)

rewrite67.0ms (1.1%)

simplify55.0ms (0.9%)

prune158.0ms (2.6%)

regimes1.4s (22.3%)

bsearch86.0ms (1.4%)

simplify3.0ms (0%)

end168.0ms (2.7%)

Profiling