Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.6s (53.9%)

Results

497.0ms	4565×	body	128	valid
457.0ms	1592×	body	512	valid
456.0ms	1351×	body	1024	valid
138.0ms	748×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

preprocess24.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
42×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	64	22
4	122	22
5	237	22
6	388	22
7	509	22
8	615	22
9	635	22
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
42×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	64	22
4	122	22
5	237	22
6	388	22
7	509	22
8	615	22
9	635	22

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series8.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))	x	inf
1.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))	x	-inf
1.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))	x	0
1.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))	x	-inf
1.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))	x	inf

rewrite70.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	273	42
2	4302	42

Stop Event

1×	node limit

Counts

3 → 127

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
263×	`associate-+l-_binary64`
251×	`associate-l_binary64`
216×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	575
1	211	559
2	601	553
3	1854	553

Stop Event

1×	node limit

Counts

163 → 167

prune124.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	165	3	168

Error

0.4b

Counts

168 → 3

Alt Table

Status	Error	Program
	31.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	10.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)

Compiler

Compiled 4050 to 3198 computations (21% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))
✓	0.3b	(cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))))
✓	0.4b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)
✓	2.5b	(-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))

series107.0ms (3.7%)

Counts

4 → 40

Calls

12 calls:

44.0ms	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)	x	-inf
26.0ms	(cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))))	x	-inf
16.0ms	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)	x	inf
9.0ms	(cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1)))))	x	inf
4.0ms	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)	x	0

rewrite90.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`log1p-udef_binary64`
184×	`egg-rr`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
161×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	81
1	352	81
2	4953	81

Stop Event

1×	node limit

Counts

4 → 184

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
398×	`unswap-sqr_binary64`
309×	`associate-/r*_binary64`
294×	`fma-def_binary64`
280×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	852
1	322	844
2	1006	838
3	3632	838

Stop Event

1×	node limit

Counts

224 → 176

prune153.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	175	4	179

Error

0.0b

Counts

179 → 4

Alt Table

Status	Error	Program
▶	31.8b	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
	31.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	10.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)

Compiler

Compiled 5147 to 4234 computations (17.7% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (cbrt.f64 2) x)
✓	0.2b	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
✓	1.0b	(cbrt.f64 2)

series65.0ms (2.2%)

Counts

3 → 12

Calls

6 calls:

18.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)	x	inf
11.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)	x	-inf
10.0ms	(/.f64 (cbrt.f64 2) x)	x	-inf
10.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)	x	0
8.0ms	(/.f64 (cbrt.f64 2) x)	x	inf

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`log1p-expm1-u_binary64`
636×	`expm1-log1p-u_binary64`
298×	`log-prod_binary64`
117×	`expm1-udef_binary64`
117×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	151	16
2	1762	16

Stop Event

1×	node limit

Counts

3 → 95

simplify60.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

568×	`sqr-pow_binary64`
456×	`associate-/r*_binary64`
362×	`unswap-sqr_binary64`
322×	`associate-/l/_binary64`
313×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	13	84
2	24	84
3	39	84
4	74	84
5	210	84
6	761	84
7	2232	84
8	2320	84
9	2453	84
10	2611	84
11	2859	84
12	3187	84
13	3608	84
14	4108	84
15	4703	84

Stop Event

1×	node limit

Counts

107 → 95

prune75.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	93	6	99

Error

0.0b

Counts

99 → 6

Alt Table

Status	Error	Program
▶	31.6b	(*.f64 2 (pow.f64 (/.f64 1 x) 3))
	31.6b	(pow.f64 (/.f64 (pow.f64 2 1/3) x) 3)
	31.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	10.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)
	31.6b	(.f64 (cbrt.f64 (/.f64 (cbrt.f64 4) (.f64 x x))) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 2) x)) (/.f64 (cbrt.f64 4) (.f64 x x))))

Compiler

Compiled 1161 to 952 computations (18% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (pow.f64 (/.f64 1 x) 3))
✓	0.2b	(pow.f64 (/.f64 1 x) 3)

series6.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(pow.f64 (/.f64 1 x) 3)	x	0
1.0ms	(*.f64 2 (pow.f64 (/.f64 1 x) 3))	x	0
1.0ms	(pow.f64 (/.f64 1 x) 3)	x	-inf
1.0ms	(*.f64 2 (pow.f64 (/.f64 1 x) 3))	x	inf
1.0ms	(*.f64 2 (pow.f64 (/.f64 1 x) 3))	x	-inf

rewrite40.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

594×	`log1p-expm1-u_binary64`
594×	`expm1-log1p-u_binary64`
295×	`log-prod_binary64`
120×	`expm1-udef_binary64`
120×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	11
2	1743	11

Stop Event

1×	node limit

Counts

2 → 48

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

729×	`sqr-pow_binary64`
625×	`associate-/l/_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	168
1	17	168
2	34	168
3	55	168
4	104	168
5	275	168
6	1018	168
7	1680	168
8	1767	168
9	1900	168
10	2058	168
11	2290	168
12	3075	168
13	3496	168
14	3996	168
15	4591	168

Stop Event

1×	node limit

Counts

72 → 48

prune35.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	49	5	54

Error

Counts

54 → 5

Alt Table

Status	Error	Program
	31.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 3)))
	31.5b	(*.f64 2 (+.f64 0 (pow.f64 x -3)))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	10.3b	(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (-.f64 (/.f64 2 x) (/.f64 1 (+.f64 x -1))))) 3)
	31.6b	(.f64 (cbrt.f64 (/.f64 (cbrt.f64 4) (.f64 x x))) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 2) x)) (/.f64 (cbrt.f64 4) (.f64 x x))))

Compiler

Compiled 531 to 442 computations (16.8% saved)

regimes127.0ms (4.4%)

Accuracy

Total 0.2b remaining (80.5%)

Threshold costs 0.2b (80.5%)

Counts

41 → 3

Compiler

Compiled 956 to 798 computations (16.5% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
0.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Steps

Iters	Point		Range
9.46923542724e-17	∈ [	9.46923542724e-17	,	76421005762251.56	]
-7.970778004113545	∈ [	-7.970778004113545	,	0.0	]

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	105
1	43	105
2	53	105
3	56	105
4	57	105

Stop Event

1×

saturated

end106.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 216 to 169 computations (21.8% saved)

Details

analyze8.0ms (0.3%)

sample1.6s (53.9%)

preprocess24.0ms (0.8%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite70.0ms (2.4%)

simplify36.0ms (1.2%)

prune124.0ms (4.3%)

localize11.0ms (0.4%)

series107.0ms (3.7%)

rewrite90.0ms (3.1%)

simplify44.0ms (1.5%)

prune153.0ms (5.3%)

localize4.0ms (0.1%)

series65.0ms (2.2%)

rewrite42.0ms (1.4%)

simplify60.0ms (2.1%)

prune75.0ms (2.6%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite40.0ms (1.4%)

simplify64.0ms (2.2%)

prune35.0ms (1.2%)

regimes127.0ms (4.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end106.0ms (3.7%)

Profiling