Details

analyze4.0ms (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
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample791.0ms (51.5%)

Results

763.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify30.0ms (2%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.2%)

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
▶	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
	0.1b	(fma.f64 (/.f64 x 6) x -1/2)

Compiler

Compiled 44 to 32 computations (27.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) 3)
✓	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)

series4.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(/.f64 (-.f64 (*.f64 x x) 3) 6)
2.0ms	(-.f64 (*.f64 x x) 3)

rewrite39.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

756×	`log1p-expm1-u_binary64`
756×	`expm1-log1p-u_binary64`
138×	`log1p-udef_binary64`
80×	`add-sqr-sqrt_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	166	13
2	2022	13

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

38.0ms	(-.f64 (*.f64 x x) 3)
38.0ms	(/.f64 (-.f64 (*.f64 x x) 3) 6)

simplify59.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
442×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
275×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	159
1	23	141
2	38	141
3	62	141
4	127	141
5	358	141
6	1247	141
7	2167	141
8	2351	141
9	2535	141
10	2743	141
11	3036	141
12	3429	141
13	3907	141
14	4468	141

Stop Event

1×	node limit

Counts

83 → 68

prune43.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Error

Counts

70 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)
✓	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
▶	0.1b	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)

Compiler

Compiled 731 to 552 computations (24.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
✓	0.2b	(*.f64 1/6 (pow.f64 x 2))

series5.0ms (0.3%)

Counts

2 → 3

Calls

2 calls:

2.0ms	(*.f64 1/6 (pow.f64 x 2))
2.0ms	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)

rewrite37.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`log1p-expm1-u_binary64`
733×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
83×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	178	15
2	1992	15

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

36.0ms	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)
36.0ms	(*.f64 1/6 (pow.f64 x 2))

simplify50.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

607×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
272×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	24	15
3	46	15
4	108	15
5	335	15
6	1240	15
7	2117	15
8	2281	15
9	2465	15
10	2673	15
11	2966	15
12	3357	15
13	3835	15
14	4396	15

Stop Event

1×	node limit

Counts

50 → 50

prune87.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	50	4	54

Error

Counts

54 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)
✓	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
▶	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
✓	0.1b	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)

Compiler

Compiled 614 to 431 computations (29.8% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)

series2.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 (/.f64 x 6) x -1/2)

rewrite31.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
273×	`unpow-prod-down_binary64`
246×	`log-prod_binary64`
156×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1488	8

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

30.0ms

(fma.f64 (/.f64 x 6) x -1/2)

simplify55.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
276×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	30	87
3	54	87
4	117	87
5	346	87
6	1211	87
7	2108	87
8	2272	87
9	2456	87
10	2664	87
11	2958	87
12	3351	87
13	3829	87
14	4390	87

Stop Event

1×	node limit

Counts

45 → 38

prune27.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	38	4	42

Error

Counts

42 → 4

Alt Table

Status	Error	Program
▶	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)
✓	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
✓	0.1b	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)

Compiler

Compiled 501 to 389 computations (22.4% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 6 (fma.f64 x x -3))
✓	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 6 (fma.f64 x x -3))
3.0ms	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

rewrite36.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
137×	`expm1-udef_binary64`
137×	`log1p-udef_binary64`
117×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	170	16
2	1922	16

Stop Event

1×	node limit

Counts

2 → 52

Calls

2 calls:

35.0ms	(/.f64 6 (fma.f64 x x -3))
35.0ms	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

simplify32.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary64`
413×	`unswap-sqr_binary64`
381×	`fma-def_binary64`
349×	`associate-l_binary64`
286×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	309
1	125	305
2	323	299
3	982	299
4	3996	299

Stop Event

1×	node limit

Counts

76 → 72

prune41.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	72	4	76

Error

Counts

76 → 4

Alt Table

Status	Error	Program
✓	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)
✓	0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
✓	0.1b	(-.f64 (*.f64 1/6 (pow.f64 x 2)) 1/2)

Compiler

Compiled 876 to 692 computations (21% saved)

regimes79.0ms (5.1%)

Accuracy

Total 0.1b remaining (89.5%)

Threshold costs 0.1b (89.5%)

Counts

23 → 1

Compiler

Compiled 812 to 618 computations (23.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

end55.0ms (3.6%)

Compiler: Compiled 46 to 35 computations (23.9% saved)

Details

analyze4.0ms (0.3%)

sample791.0ms (51.5%)

simplify30.0ms (2%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.3%)

rewrite39.0ms (2.6%)

simplify59.0ms (3.9%)

prune43.0ms (2.8%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite37.0ms (2.4%)

simplify50.0ms (3.3%)

prune87.0ms (5.7%)

localize3.0ms (0.2%)

series2.0ms (0.2%)

rewrite31.0ms (2%)

simplify55.0ms (3.6%)

prune27.0ms (1.8%)

localize4.0ms (0.3%)

series7.0ms (0.4%)

rewrite36.0ms (2.3%)

simplify32.0ms (2.1%)

prune41.0ms (2.7%)

regimes79.0ms (5.1%)

simplify2.0ms (0.1%)

end55.0ms (3.6%)

Profiling