Details

analyze118.0ms (2.2%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.9s (36.1%)

Results

1.7s	8256×	body	128	valid
42.0ms	228×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify207.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1205×	`fma-neg_binary64`
900×	`fma-def_binary64`
326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	145	16
4	257	16
5	411	16
6	861	16
7	1371	16
8	2386	16
9	2493	16
10	2675	16
11	2607	16
12	2581	16
13	2581	16
14	3531	16
15	3364	16
16	3364	16
17	3364	16
18	3364	16
19	3171	16

prune7.0ms (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 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(/.f64 1 (*.f64 x 9))
✓	0.3b	(*.f64 3 (sqrt.f64 x))

series70.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

46.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
11.0ms	(*.f64 3 (sqrt.f64 x))
9.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite114.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
226×	`log1p-udef_binary64`
225×	`expm1-udef_binary64`
134×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`

Counts

4 → 102

Calls

4 calls:

103.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
103.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
103.0ms	(/.f64 1 (*.f64 x 9))
103.0ms	(*.f64 3 (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	282	35
2	3333	35
3	5120	35
0	0	0
1	0	0

simplify154.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

985×	`fma-def_binary64`
640×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
202×	`distribute-lft-in_binary64`

Counts

150 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	453
1	54	408
2	106	387
3	186	387
4	358	387
5	544	387
6	1055	387
7	1692	387
8	2031	387
9	2091	387
10	2032	387
11	2032	387
12	2393	387
13	2393	387
14	2393	387
15	2248	387

prune230.0ms (4.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Error

0.0b

Counts

115 → 11

Alt Table

Status	Error	Program
	1.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) 3) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	19.8b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
▶	0.3b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.7b	(.f64 (pow.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	27.5b	(/.f64 (.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (.f64 3 (sqrt.f64 x))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	16.8b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x x) 81)) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) 1))
	0.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (cbrt.f64 (/.f64 1/9 x)) (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 2))) 1))

Compiler

Compiled 2376 to 1742 computations (26.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.1b	(sqrt.f64 (*.f64 x 9))
✓	0.2b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.3b	(/.f64 1 (*.f64 x 9))

series55.0ms (1%)

Counts

2 → 12

Calls

2 calls:

45.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
10.0ms	(sqrt.f64 (*.f64 x 9))

rewrite97.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
350×	`fma-def_binary64`
218×	`fma-neg_binary64`
201×	`log1p-udef_binary64`
200×	`expm1-udef_binary64`

Counts

2 → 54

Calls

2 calls:

95.0ms	(sqrt.f64 (*.f64 x 9))
95.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	243	24
2	2990	24
3	4918	24
0	0	0
1	0	0

simplify158.0ms (3%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
760×	`fma-def_binary64`
230×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
201×	`distribute-lft-in_binary64`

Counts

66 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	267
1	52	222
2	102	201
3	182	201
4	354	201
5	540	201
6	1051	201
7	1688	201
8	2019	201
9	2255	201
10	2197	201
11	2197	201
12	2335	201
13	2335	201
14	2335	201
15	2335	201
16	2190	201

prune249.0ms (4.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	130	10	140

Error

0.0b

Counts

140 → 10

Alt Table

Status	Error	Program
	0.7b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 3)) 1))
✓	0.3b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	19.8b	(.f64 (cbrt.f64 (pow.f64 (.f64 x 9) 3/2)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (pow.f64 (pow.f64 (.f64 x 9) 1/4) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
▶	0.4b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
	27.5b	(/.f64 (.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (.f64 3 (sqrt.f64 x))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	16.8b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x x) 81)) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) 1))

Compiler

Compiled 2592 to 2011 computations (22.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (*.f64 1/9 (/.f64 1 x)))
	0.1b	(sqrt.f64 (*.f64 x 9))
✓	0.2b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
✓	0.4b	(*.f64 1/9 (/.f64 1 x))

series62.0ms (1.2%)

Counts

3 → 30

Calls

3 calls:

46.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
10.0ms	(+.f64 y (*.f64 1/9 (/.f64 1 x)))
6.0ms	(*.f64 1/9 (/.f64 1 x))

rewrite94.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

881×	`prod-diff_binary64`
132×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
127×	`add-cbrt-cube_binary64`

Counts

3 → 82

Calls

3 calls:

91.0ms	(+.f64 y (*.f64 1/9 (/.f64 1 x)))
91.0ms	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
91.0ms	(*.f64 1/9 (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	285	29
2	3367	29
3	4928	29
0	0	0
1	0	0

simplify148.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
760×	`fma-def_binary64`
230×	`distribute-rgt-in_binary64`
221×	`distribute-rgt-neg-in_binary64`
201×	`distribute-lft-in_binary64`

Counts

112 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	327
1	52	282
2	102	261
3	182	261
4	354	261
5	540	261
6	1051	261
7	1688	261
8	2019	261
9	2255	261
10	2197	261
11	2197	261
12	2335	261
13	2335	261
14	2335	261
15	2335	261
16	2190	261

prune202.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	118	9	127

Error

0.0b

Counts

127 → 9

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.4b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	19.8b	(.f64 (cbrt.f64 (pow.f64 (.f64 x 9) 3/2)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (pow.f64 (pow.f64 (.f64 x 9) 1/4) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.4b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
	27.5b	(/.f64 (.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) -1) (.f64 3 (sqrt.f64 x))) (+.f64 1 (+.f64 (/.f64 1/9 x) y)))
	0.5b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)) y) 1))

Compiler

Compiled 2339 to 1780 computations (23.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.3b	(.f64 3 (.f64 y (sqrt.f64 x)))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series53.0ms (1%)

Counts

3 → 0

Calls

3 calls:

24.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
17.0ms	(*.f64 y (sqrt.f64 x))
12.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite76.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

515×	`log-prod_binary64`
301×	`pow2_binary64`
193×	`pow-unpow_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`

Counts

3 → 56

Calls

3 calls:

74.0ms	(*.f64 y (sqrt.f64 x))
74.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
74.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	239	21
2	2515	21
3	5133	21
0	0	0
1	0	0

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune124.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Error

0.0b

Counts

80 → 8

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.4b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	19.8b	(.f64 (cbrt.f64 (pow.f64 (.f64 x 9) 3/2)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (pow.f64 (pow.f64 (.f64 x 9) 1/4) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.4b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (*.f64 1/9 (/.f64 1 x))) 1))
	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 1632 to 1073 computations (34.3% saved)

regimes832.0ms (15.8%)

Accuracy

Total 0.3b remaining (90.2%)

Threshold costs 0.3b (90.2%)

Counts

149 → 1

Compiler

Compiled 7673 to 6181 computations (19.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	19	21
2	20	21
3	18	21

end226.0ms (4.3%)

Compiler: Compiled 171 to 134 computations (21.6% saved)

Details

analyze118.0ms (2.2%)

sample1.9s (36.1%)

simplify207.0ms (3.9%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

series70.0ms (1.3%)

rewrite114.0ms (2.2%)

simplify154.0ms (2.9%)

prune230.0ms (4.4%)

localize14.0ms (0.3%)

series55.0ms (1%)

rewrite97.0ms (1.8%)

simplify158.0ms (3%)

prune249.0ms (4.7%)

localize16.0ms (0.3%)

series62.0ms (1.2%)

rewrite94.0ms (1.8%)

simplify148.0ms (2.8%)

prune202.0ms (3.8%)

localize22.0ms (0.4%)

series53.0ms (1%)

rewrite76.0ms (1.4%)

simplify11.0ms (0.2%)

prune124.0ms (2.4%)

regimes832.0ms (15.8%)

simplify4.0ms (0.1%)

end226.0ms (4.3%)

Profiling