Details

analyze879.0ms (14.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
18.7%	70.2%	11.1%	11
21.1%	66.7%	12.3%	12
31.6%	55.9%	12.5%	13
34.5%	52.3%	13.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (18.6%)

Results

881.0ms	8256×	body	128	valid
201.0ms	1850×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`fma-def_binary64`
8×	`+-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	25	9
3	38	9
4	52	9
5	52	9

prune3.0ms (0%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)

Compiler

Compiled 46 to 26 computations (43.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x y) z)
✓	0.1b	(.f64 (+.f64 (.f64 x y) z) y)

series14.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

9.0ms	(.f64 (+.f64 (.f64 x y) z) y)
5.0ms	(+.f64 (*.f64 x y) z)

rewrite53.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

811×	`prod-diff_binary64`
754×	`log1p-expm1-u_binary64`
754×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
71×	`add-log-exp_binary64`

Counts

2 → 60

Calls

2 calls:

51.0ms	(+.f64 (*.f64 x y) z)
51.0ms	(.f64 (+.f64 (.f64 x y) z) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	149	13
2	1917	13
3	6164	13
0	0	0
1	0	0

simplify163.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

804×	`sqr-pow_binary64`
546×	`associate-l_binary64`
539×	`cube-prod_binary64`
492×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Counts

132 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	507
1	23	507
2	35	426
3	61	426
4	129	426
5	323	426
6	995	426
7	1653	426
8	1790	426
9	1946	426
10	2126	426
11	2307	426
12	2524	426
13	2713	426
14	3132	426
15	3697	426
16	4383	426
17	4601	426
18	4845	426
19	4703	426

prune47.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y) t)
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
	2.5b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)

Compiler

Compiled 1022 to 412 computations (59.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y)
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) z)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
✓	12.8b	(cbrt.f64 (*.f64 x y))

series2.5s (41%)

Counts

4 → 120

Calls

4 calls:

880.0ms	(.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y)
824.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) z)
390.0ms	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
367.0ms	(cbrt.f64 (*.f64 x y))

rewrite65.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
214×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`

Counts

4 → 85

Calls

4 calls:

63.0ms	(.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y)
63.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (.f64 x y)) z)
63.0ms	(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
63.0ms	(cbrt.f64 (*.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	198	26
2	2105	26
3	5197	26
0	0	0
1	0	0

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

774×	`associate-l_binary64`
699×	`associate-r_binary64`
440×	`unswap-sqr_binary64`
434×	`prod-exp_binary64`
249×	`fma-def_binary64`

Counts

205 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	2270
1	177	2270
2	304	1976
3	909	994
4	3751	962
5	4234	962
6	4928	962

prune88.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Error

0.0b

Counts

156 → 3

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y) t)
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
▶	2.5b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)

Compiler

Compiled 2660 to 1152 computations (56.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x))
✓	7.4b	(*.f64 (pow.f64 y 2) x)

series20.0ms (0.3%)

Counts

2 → 9

Calls

2 calls:

12.0ms	(+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x))
8.0ms	(*.f64 (pow.f64 y 2) x)

rewrite52.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`
87×	`add-cube-cbrt_binary64`

Counts

2 → 52

Calls

2 calls:

51.0ms	(+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x))
51.0ms	(*.f64 (pow.f64 y 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	192	18
2	2249	18
3	5304	18
0	0	0
1	0	0

simplify152.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1127×	`sqr-pow_binary64`
577×	`fabs-mul_binary64`
564×	`cube-prod_binary64`
541×	`pow-sqr_binary64`
523×	`associate-l_binary64`

Counts

61 → 55

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	51
1	15	51
2	25	51
3	48	51
4	103	51
5	258	51
6	800	51
7	1203	51
8	1308	51
9	1464	51
10	1644	51
11	1825	51
12	2048	51
13	2215	51
14	2634	51
15	3199	51
16	3885	51
17	4103	51
18	4347	51
19	4429	51
20	4462	51
21	4483	51
22	5052	51

prune38.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	54	4	58

Error

0.0b

Counts

58 → 4

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y) t)
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
▶	32.5b	(+.f64 (/.f64 1 (/.f64 (-.f64 (.f64 y z) (.f64 (.f64 y y) x)) (-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (.f64 x x))))) t)
✓	2.5b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)

Compiler

Compiled 1062 to 357 computations (66.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (*.f64 x x)))
✓	7.4b	(.f64 (.f64 y y) x)
✓	16.3b	(.f64 (pow.f64 y 4) (.f64 x x))
✓	26.8b	(/.f64 (-.f64 (.f64 y z) (.f64 (.f64 y y) x)) (-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (.f64 x x))))

series94.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

36.0ms	(-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (*.f64 x x)))
35.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 (.f64 y y) x)) (-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (.f64 x x))))
15.0ms	(.f64 (pow.f64 y 4) (.f64 x x))
9.0ms	(.f64 (.f64 y y) x)

rewrite93.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

297×	`log1p-udef_binary64`
175×	`add-sqr-sqrt_binary64`
175×	`log1p-expm1-u_binary64`
175×	`expm1-log1p-u_binary64`
168×	`add-cube-cbrt_binary64`

Counts

4 → 106

Calls

4 calls:

90.0ms	(-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (*.f64 x x)))
90.0ms	(.f64 (.f64 y y) x)
90.0ms	(.f64 (pow.f64 y 4) (.f64 x x))
90.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 (.f64 y y) x)) (-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (.f64 x x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	70
1	367	49
2	4553	49
3	4951	49
0	0	0
1	0	0

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

854×	`cancel-sign-sub-inv_binary64`
564×	`unswap-sqr_binary64`
424×	`fma-def_binary64`
357×	`fma-neg_binary64`
292×	`times-frac_binary64`

Counts

226 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	2209
1	139	2209
2	457	2165
3	2241	2165
4	5066	2165

prune99.0ms (1.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	131	4	135

Error

0.0b

Counts

135 → 4

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (cbrt.f64 (*.f64 x y)) z) y) t)
✓	0.0b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
✓	32.5b	(+.f64 (/.f64 1 (/.f64 (-.f64 (.f64 y z) (.f64 (.f64 y y) x)) (-.f64 (pow.f64 (.f64 y z) 2) (.f64 (pow.f64 y 4) (.f64 x x))))) t)
✓	2.5b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)

Compiler

Compiled 4256 to 1979 computations (53.5% saved)

regimes172.0ms (2.9%)

Accuracy

Total 0.0b remaining (52.3%)

Threshold costs 0.0b (52.3%)

Counts

32 → 1

Compiler

Compiled 3160 to 1958 computations (38% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	13	13

end169.0ms (2.8%)

Compiler: Compiled 105 to 64 computations (39% saved)

Details

analyze879.0ms (14.6%)

sample1.1s (18.6%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series14.0ms (0.2%)

rewrite53.0ms (0.9%)

simplify163.0ms (2.7%)

prune47.0ms (0.8%)

localize10.0ms (0.2%)

series2.5s (41%)

rewrite65.0ms (1.1%)

simplify102.0ms (1.7%)

prune88.0ms (1.5%)

localize8.0ms (0.1%)

series20.0ms (0.3%)

rewrite52.0ms (0.9%)

simplify152.0ms (2.5%)

prune38.0ms (0.6%)

localize15.0ms (0.3%)

series94.0ms (1.6%)

rewrite93.0ms (1.5%)

simplify71.0ms (1.2%)

prune99.0ms (1.7%)

regimes172.0ms (2.9%)

simplify2.0ms (0%)

end169.0ms (2.8%)

Profiling