Details

analyze71.0ms (2.1%)

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)

sample1.1s (33.1%)

Results

969.0ms	8256×	body	128	valid
21.0ms	204×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify180.0ms (5.3%)

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

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 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)

localize10.0ms (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 3 (sqrt.f64 x))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series36.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

24.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite75.0ms (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 → 106

Calls

4 calls:

74.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
74.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
74.0ms	(*.f64 3 (sqrt.f64 x))
74.0ms	(/.f64 1 (*.f64 x 9))

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

simplify122.0ms (3.6%)

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

154 → 115

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

prune120.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	107	10	117

Error

0.0b

Counts

117 → 10

Alt Table

Status	Error	Program
	26.7b	(/.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)))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	16.7b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) -1) (pow.f64 (*.f64 3 (sqrt.f64 x)) -1))) 1))
	48.9b	(sqrt.f64 (.f64 (.f64 x 9) (pow.f64 (+.f64 (/.f64 1/9 x) (-.f64 y 1)) 2)))
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	34.9b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (/.f64 1 (/.f64 (fma.f64 y y (.f64 (/.f64 1/9 x) (-.f64 (/.f64 1/9 x) y))) (+.f64 (pow.f64 (.f64 x 9) -3) (pow.f64 y 3)))) 1))

Compiler

Compiled 2364 to 1721 computations (27.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.8%)

Counts

3 → 0

Calls

3 calls:

11.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 x))
6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite52.0ms (1.5%)

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 → 58

Calls

3 calls:

51.0ms	(*.f64 y (sqrt.f64 x))
51.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
51.0ms	(*.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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune84.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Error

0.0b

Counts

84 → 10

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	0.7b	(-.f64 (+.f64 (.f64 3 (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) 3)) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	26.7b	(/.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)))
✓	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	16.7b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) -1) (pow.f64 (*.f64 3 (sqrt.f64 x)) -1))) 1))
	48.9b	(sqrt.f64 (.f64 (.f64 x 9) (pow.f64 (+.f64 (/.f64 1/9 x) (-.f64 y 1)) 2)))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))

Compiler

Compiled 1891 to 1272 computations (32.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y -3)
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series29.0ms (0.8%)

Counts

3 → 24

Calls

3 calls:

23.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
4.0ms	(sqrt.f64 (/.f64 1 x))
2.0ms	(fma.f64 3 y -3)

rewrite59.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

487×	`log-prod_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
204×	`pow1/3_binary64`
187×	`pow3_binary64`

Counts

3 → 92

Calls

3 calls:

57.0ms	(fma.f64 3 y -3)
57.0ms	(sqrt.f64 (/.f64 1 x))
57.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	259	25
2	2652	25
3	4894	25
0	0	0
1	0	0

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
467×	`fma-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`
73×	`distribute-rgt-neg-in_binary64`
51×	`sub-neg_binary64`

Counts

116 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	323
1	43	258
2	73	258
3	120	258
4	202	258
5	295	258
6	538	258
7	799	258
8	940	258
9	1059	258
10	1066	258
11	983	258

prune140.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	2	5	7
Picked	1	0	1
Done	1	1	2
Total	120	10	130

Error

0.0b

Counts

130 → 10

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	0.7b	(-.f64 (+.f64 (.f64 3 (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) 3)) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
▶	0.3b	(pow.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x))) 1)
	26.7b	(/.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)))
✓	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.5b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	18.5b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.8b	(fma.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (fma.f64 3 y -3)) 3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	48.9b	(sqrt.f64 (.f64 (.f64 x 9) (pow.f64 (+.f64 (/.f64 1/9 x) (-.f64 y 1)) 2)))
	13.8b	(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y -3)) (.f64 (sqrt.f64 x) (fma.f64 3 y -3))) (.f64 (/.f64 1 x) 1/9)) (-.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 y -3)) (/.f64 1/3 (sqrt.f64 x))))

Compiler

Compiled 2358 to 1663 computations (29.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 3 y -3)
✓	0.2b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
✓	0.4b	(/.f64 1/3 (sqrt.f64 x))

series34.0ms (1%)

Counts

2 → 12

Calls

2 calls:

22.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
12.0ms	(/.f64 1/3 (sqrt.f64 x))

rewrite54.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
112×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-log-exp_binary64`

Counts

2 → 47

Calls

2 calls:

53.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x)))
53.0ms	(/.f64 1/3 (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	208	22
2	2252	22
3	5372	22
0	0	0
1	0	0

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
467×	`fma-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`
73×	`distribute-rgt-neg-in_binary64`
51×	`sub-neg_binary64`

Counts

59 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	269
1	39	222
2	69	204
3	119	204
4	202	204
5	295	204
6	538	204
7	799	204
8	940	204
9	1059	204
10	1066	204
11	983	204

prune93.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	84	10	94

Error

0.0b

Counts

94 → 10

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3)
	0.7b	(-.f64 (+.f64 (.f64 3 (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) 3)) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
✓	0.3b	(pow.f64 (fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (/.f64 1/3 (sqrt.f64 x))) 1)
	26.7b	(/.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)))
✓	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.5b	(.f64 (sqrt.f64 (.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	18.5b	(fma.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.8b	(fma.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (fma.f64 3 y -3)) 3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	48.9b	(sqrt.f64 (.f64 (.f64 x 9) (pow.f64 (+.f64 (/.f64 1/9 x) (-.f64 y 1)) 2)))
	13.8b	(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 x) (fma.f64 3 y -3)) (.f64 (sqrt.f64 x) (fma.f64 3 y -3))) (.f64 (/.f64 1 x) 1/9)) (-.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 y -3)) (/.f64 1/3 (sqrt.f64 x))))

Compiler

Compiled 1646 to 1142 computations (30.6% saved)

regimes764.0ms (22.4%)

Accuracy

Total 0.3b remaining (93.6%)

Threshold costs 0.3b (93.6%)

Counts

147 → 1

Compiler

Compiled 7472 to 5875 computations (21.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	28	28
2	35	28
3	39	28
4	42	28
5	43	28
6	41	28

end199.0ms (5.8%)

Compiler: Compiled 243 to 188 computations (22.6% saved)

Details

analyze71.0ms (2.1%)

sample1.1s (33.1%)

simplify180.0ms (5.3%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

series36.0ms (1.1%)

rewrite75.0ms (2.2%)

simplify122.0ms (3.6%)

prune120.0ms (3.5%)

localize13.0ms (0.4%)

series27.0ms (0.8%)

rewrite52.0ms (1.5%)

simplify6.0ms (0.2%)

prune84.0ms (2.5%)

localize10.0ms (0.3%)

series29.0ms (0.8%)

rewrite59.0ms (1.7%)

simplify47.0ms (1.4%)

prune140.0ms (4.1%)

localize8.0ms (0.2%)

series34.0ms (1%)

rewrite54.0ms (1.6%)

simplify44.0ms (1.3%)

prune93.0ms (2.7%)

regimes764.0ms (22.4%)

simplify3.0ms (0.1%)

end199.0ms (5.8%)

Profiling